Daily Papers

Evaluating the performance of perception modules in autonomous driving is one of the most critical tasks in developing the complex intelligent system. While module-level unit test metrics adopted from traditional computer vision tasks are feasible to some extent, it remains far less explored to measure the impact of perceptual noise on the driving quality of autonomous vehicles in a consistent and holistic manner. In this work, we propose a principled framework that provides a coherent and systematic understanding of the impact an error in the perception module imposes on an autonomous agent's planning that actually controls the vehicle. Specifically, the planning process is formulated as expected utility maximisation, where all input signals from upstream modules jointly provide a world state description, and the planner strives for the optimal action by maximising the expected utility determined by both world states and actions. We show that, under practical conditions, the objective function can be represented as an inner product between the world state description and the utility function in a Hilbert space. This geometric interpretation enables a novel way to analyse the impact of noise in world state estimation on planning and leads to a universal metric for evaluating perception. The whole framework resembles the idea of transcendental idealism in the classical philosophical literature, which gives the name to our approach.

We present Diffusion-KTO, a novel approach for aligning text-to-image diffusion models by formulating the alignment objective as the maximization of expected human utility. Since this objective applies to each generation independently, Diffusion-KTO does not require collecting costly pairwise preference data nor training a complex reward model. Instead, our objective requires simple per-image binary feedback signals, e.g. likes or dislikes, which are abundantly available. After fine-tuning using Diffusion-KTO, text-to-image diffusion models exhibit superior performance compared to existing techniques, including supervised fine-tuning and Diffusion-DPO, both in terms of human judgment and automatic evaluation metrics such as PickScore and ImageReward. Overall, Diffusion-KTO unlocks the potential of leveraging readily available per-image binary signals and broadens the applicability of aligning text-to-image diffusion models with human preferences.

Risk-averse reinforcement learning finds application in various high-stakes fields. Unlike classical reinforcement learning, which aims to maximize expected returns, risk-averse agents choose policies that minimize risk, occasionally sacrificing expected value. These preferences can be framed through utility theory. We focus on the specific case of the exponential utility function, where we can derive the Bellman equations and employ various reinforcement learning algorithms with few modifications. However, these methods suffer from numerical instability due to the need for exponent computation throughout the process. To address this, we introduce a numerically stable and mathematically sound loss function based on the Itakura-Saito divergence for learning state-value and action-value functions. We evaluate our proposed loss function against established alternatives, both theoretically and empirically. In the experimental section, we explore multiple financial scenarios, some with known analytical solutions, and show that our loss function outperforms the alternatives.

Existing preference optimization methods are mainly designed for directly learning from human feedback with the assumption that paired examples (preferred vs. dis-preferred) are available. In contrast, we propose a method that can leverage unpaired preferred or dis-preferred examples, and works even when only one type of feedback (positive or negative) is available. This flexibility allows us to apply it in scenarios with varying forms of feedback and models, including training generative language models based on human feedback as well as training policies for sequential decision-making problems, where learned (value) functions are available. Our approach builds upon the probabilistic framework introduced in (Dayan and Hinton, 1997), which proposes to use expectation-maximization (EM) to directly optimize the probability of preferred outcomes (as opposed to classic expected reward maximization). To obtain a practical algorithm, we identify and address a key limitation in current EM-based methods: when applied to preference optimization, they solely maximize the likelihood of preferred examples, while neglecting dis-preferred samples. We show how one can extend EM algorithms to explicitly incorporate dis-preferred outcomes, leading to a novel, theoretically grounded, preference optimization algorithm that offers an intuitive and versatile way to learn from both positive and negative feedback.

In this paper we argue for the fundamental importance of the value distribution: the distribution of the random return received by a reinforcement learning agent. This is in contrast to the common approach to reinforcement learning which models the expectation of this return, or value. Although there is an established body of literature studying the value distribution, thus far it has always been used for a specific purpose such as implementing risk-aware behaviour. We begin with theoretical results in both the policy evaluation and control settings, exposing a significant distributional instability in the latter. We then use the distributional perspective to design a new algorithm which applies Bellman's equation to the learning of approximate value distributions. We evaluate our algorithm using the suite of games from the Arcade Learning Environment. We obtain both state-of-the-art results and anecdotal evidence demonstrating the importance of the value distribution in approximate reinforcement learning. Finally, we combine theoretical and empirical evidence to highlight the ways in which the value distribution impacts learning in the approximate setting.

We introduce distributional dynamic programming (DP) methods for optimizing statistical functionals of the return distribution, with standard reinforcement learning as a special case. Previous distributional DP methods could optimize the same class of expected utilities as classic DP. To go beyond expected utilities, we combine distributional DP with stock augmentation, a technique previously introduced for classic DP in the context of risk-sensitive RL, where the MDP state is augmented with a statistic of the rewards obtained so far (since the first time step). We find that a number of recently studied problems can be formulated as stock-augmented return distribution optimization, and we show that we can use distributional DP to solve them. We analyze distributional value and policy iteration, with bounds and a study of what objectives these distributional DP methods can or cannot optimize. We describe a number of applications outlining how to use distributional DP to solve different stock-augmented return distribution optimization problems, for example maximizing conditional value-at-risk, and homeostatic regulation. To highlight the practical potential of stock-augmented return distribution optimization and distributional DP, we combine the core ideas of distributional value iteration with the deep RL agent DQN, and empirically evaluate it for solving instances of the applications discussed.

Implementing a reward function that perfectly captures a complex task in the real world is impractical. As a result, it is often appropriate to think of the reward function as a proxy for the true objective rather than as its definition. We study this phenomenon through the lens of Goodhart's law, which predicts that increasing optimisation of an imperfect proxy beyond some critical point decreases performance on the true objective. First, we propose a way to quantify the magnitude of this effect and show empirically that optimising an imperfect proxy reward often leads to the behaviour predicted by Goodhart's law for a wide range of environments and reward functions. We then provide a geometric explanation for why Goodhart's law occurs in Markov decision processes. We use these theoretical insights to propose an optimal early stopping method that provably avoids the aforementioned pitfall and derive theoretical regret bounds for this method. Moreover, we derive a training method that maximises worst-case reward, for the setting where there is uncertainty about the true reward function. Finally, we evaluate our early stopping method experimentally. Our results support a foundation for a theoretically-principled study of reinforcement learning under reward misspecification.

The performance of acquisition functions for Bayesian optimisation to locate the global optimum of continuous functions is investigated in terms of the Pareto front between exploration and exploitation. We show that Expected Improvement (EI) and the Upper Confidence Bound (UCB) always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is not guaranteed to do so and Weighted Expected Improvement does so only for a restricted range of weights. We introduce two novel epsilon-greedy acquisition functions. Extensive empirical evaluation of these together with random search, purely exploratory, and purely exploitative search on 10 benchmark problems in 1 to 10 dimensions shows that epsilon-greedy algorithms are generally at least as effective as conventional acquisition functions (e.g., EI and UCB), particularly with a limited budget. In higher dimensions epsilon-greedy approaches are shown to have improved performance over conventional approaches. These results are borne out on a real world computational fluid dynamics optimisation problem and a robotics active learning problem. Our analysis and experiments suggest that the most effective strategy, particularly in higher dimensions, is to be mostly greedy, occasionally selecting a random exploratory solution.

When trying to solve a computational problem, we are often faced with a choice between algorithms that are guaranteed to return the right answer but differ in their runtime distributions (e.g., SAT solvers, sorting algorithms). This paper aims to lay theoretical foundations for such choices by formalizing preferences over runtime distributions. It might seem that we should simply prefer the algorithm that minimizes expected runtime. However, such preferences would be driven by exactly how slow our algorithm is on bad inputs, whereas in practice we are typically willing to cut off occasional, sufficiently long runs before they finish. We propose a principled alternative, taking a utility-theoretic approach to characterize the scoring functions that describe preferences over algorithms. These functions depend on the way our value for solving our problem decreases with time and on the distribution from which captimes are drawn. We describe examples of realistic utility functions and show how to leverage a maximum-entropy approach for modeling underspecified captime distributions. Finally, we show how to efficiently estimate an algorithm's expected utility from runtime samples.

We seek to understand fundamental tradeoffs between the accuracy of prior information that a learner has on a given problem and its learning performance. We introduce the notion of prioritized risk, which differs from traditional notions of minimax and Bayes risk by allowing us to study such fundamental tradeoffs in settings where reality does not necessarily conform to the learner's prior. We present a general reduction-based approach for extending classical minimax lower-bound techniques in order to lower bound the prioritized risk for statistical estimation problems. We also introduce a novel generalization of Fano's inequality (which may be of independent interest) for lower bounding the prioritized risk in more general settings involving unbounded losses. We illustrate the ability of our framework to provide insights into tradeoffs between prior information and learning performance for problems in estimation, regression, and reinforcement learning.

Many classic Reinforcement Learning (RL) algorithms rely on a Bellman operator, which involves an expectation over the next states, leading to the concept of bootstrapping. To introduce a form of pessimism, we propose to replace this expectation with an expectile. In practice, this can be very simply done by replacing the L_2 loss with a more general expectile loss for the critic. Introducing pessimism in RL is desirable for various reasons, such as tackling the overestimation problem (for which classic solutions are double Q-learning or the twin-critic approach of TD3) or robust RL (where transitions are adversarial). We study empirically these two cases. For the overestimation problem, we show that the proposed approach, ExpectRL, provides better results than a classic twin-critic. On robust RL benchmarks, involving changes of the environment, we show that our approach is more robust than classic RL algorithms. We also introduce a variation of ExpectRL combined with domain randomization which is competitive with state-of-the-art robust RL agents. Eventually, we also extend \ExpectRL with a mechanism for choosing automatically the expectile value, that is the degree of pessimism

We study mean field portfolio games under Epstein-Zin preferences, which naturally encompass the classical time-additive power utility as a special case. In a general non-Markovian framework, we establish a uniqueness result by proving a one-to-one correspondence between Nash equilibria and the solutions to a class of BSDEs. A key ingredient in our approach is a necessary stochastic maximum principle tailored to Epstein-Zin utility and a nonlinear transformation. In the deterministic setting, we further derive an explicit closed-form solution for the equilibrium investment and consumption policies.

Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo methods can be costly to do so. We propose here a new procedure based on importance sampling and control variates for estimating more efficiently multiple expectations with the same sample. We first show that there exists a family of optimal estimators combining both importance sampling and control variates, which however cannot be used in practice because they require the knowledge of the values of the expectations to estimate. Motivated by the form of these optimal estimators and some interesting properties, we therefore propose an adaptive algorithm. The general idea is to adaptively update the parameters of the estimators for approaching the optimal ones. We suggest then a quantitative stopping criterion that exploits the trade-off between approaching these optimal parameters and having a sufficient budget left. This left budget is then used to draw a new independent sample from the final sampling distribution, allowing to get unbiased estimators of the expectations. We show how to apply our procedure to sensitivity analysis, by estimating Sobol' indices and quantifying the impact of the input distributions. Finally, realistic test cases show the practical interest of the proposed algorithm, and its significant improvement over estimating the expectations separately.

The dominant practice of AI alignment assumes (1) that preferences are an adequate representation of human values, (2) that human rationality can be understood in terms of maximizing the satisfaction of preferences, and (3) that AI systems should be aligned with the preferences of one or more humans to ensure that they behave safely and in accordance with our values. Whether implicitly followed or explicitly endorsed, these commitments constitute what we term a preferentist approach to AI alignment. In this paper, we characterize and challenge the preferentist approach, describing conceptual and technical alternatives that are ripe for further research. We first survey the limits of rational choice theory as a descriptive model, explaining how preferences fail to capture the thick semantic content of human values, and how utility representations neglect the possible incommensurability of those values. We then critique the normativity of expected utility theory (EUT) for humans and AI, drawing upon arguments showing how rational agents need not comply with EUT, while highlighting how EUT is silent on which preferences are normatively acceptable. Finally, we argue that these limitations motivate a reframing of the targets of AI alignment: Instead of alignment with the preferences of a human user, developer, or humanity-writ-large, AI systems should be aligned with normative standards appropriate to their social roles, such as the role of a general-purpose assistant. Furthermore, these standards should be negotiated and agreed upon by all relevant stakeholders. On this alternative conception of alignment, a multiplicity of AI systems will be able to serve diverse ends, aligned with normative standards that promote mutual benefit and limit harm despite our plural and divergent values.

Bayesian optimisation is a popular approach for optimising expensive black-box functions. The next location to be evaluated is selected via maximising an acquisition function that balances exploitation and exploration. Gaussian processes, the surrogate models of choice in Bayesian optimisation, are often used with a constant prior mean function equal to the arithmetic mean of the observed function values. We show that the rate of convergence can depend sensitively on the choice of mean function. We empirically investigate 8 mean functions (constant functions equal to the arithmetic mean, minimum, median and maximum of the observed function evaluations, linear, quadratic polynomials, random forests and RBF networks), using 10 synthetic test problems and two real-world problems, and using the Expected Improvement and Upper Confidence Bound acquisition functions. We find that for design dimensions ge5 using a constant mean function equal to the worst observed quality value is consistently the best choice on the synthetic problems considered. We argue that this worst-observed-quality function promotes exploitation leading to more rapid convergence. However, for the real-world tasks the more complex mean functions capable of modelling the fitness landscape may be effective, although there is no clearly optimum choice.

Utility functions or their equivalents (value functions, objective functions, loss functions, reward functions, preference orderings) are a central tool in most current machine learning systems. These mechanisms for defining goals and guiding optimization run into practical and conceptual difficulty when there are independent, multi-dimensional objectives that need to be pursued simultaneously and cannot be reduced to each other. Ethicists have proved several impossibility theorems that stem from this origin; those results appear to show that there is no way of formally specifying what it means for an outcome to be good for a population without violating strong human ethical intuitions (in such cases, the objective function is a social welfare function). We argue that this is a practical problem for any machine learning system (such as medical decision support systems or autonomous weapons) or rigidly rule-based bureaucracy that will make high stakes decisions about human lives: such systems should not use objective functions in the strict mathematical sense. We explore the alternative of using uncertain objectives, represented for instance as partially ordered preferences, or as probability distributions over total orders. We show that previously known impossibility theorems can be transformed into uncertainty theorems in both of those settings, and prove lower bounds on how much uncertainty is implied by the impossibility results. We close by proposing two conjectures about the relationship between uncertainty in objectives and severe unintended consequences from AI systems.

In risk-averse reinforcement learning (RL), the goal is to optimize some risk measure of the returns. A risk measure often focuses on the worst returns out of the agent's experience. As a result, standard methods for risk-averse RL often ignore high-return strategies. We prove that under certain conditions this inevitably leads to a local-optimum barrier, and propose a soft risk mechanism to bypass it. We also devise a novel Cross Entropy module for risk sampling, which (1) preserves risk aversion despite the soft risk; (2) independently improves sample efficiency. By separating the risk aversion of the sampler and the optimizer, we can sample episodes with poor conditions, yet optimize with respect to successful strategies. We combine these two concepts in CeSoR - Cross-entropy Soft-Risk optimization algorithm - which can be applied on top of any risk-averse policy gradient (PG) method. We demonstrate improved risk aversion in maze navigation, autonomous driving, and resource allocation benchmarks, including in scenarios where standard risk-averse PG completely fails.

In this paper, we introduce the Preselection Bandit problem, in which the learner preselects a subset of arms (choice alternatives) for a user, which then chooses the final arm from this subset. The learner is not aware of the user's preferences, but can learn them from observed choices. In our concrete setting, we allow these choices to be stochastic and model the user's actions by means of the Plackett-Luce model. The learner's main task is to preselect subsets that eventually lead to highly preferred choices. To formalize this goal, we introduce a reasonable notion of regret and derive lower bounds on the expected regret. Moreover, we propose algorithms for which the upper bound on expected regret matches the lower bound up to a logarithmic term of the time horizon.

It is typically understood that the training of modern neural networks is a process of fitting the probability distribution of desired output. However, recent paradoxical observations in a number of language generation tasks let one wonder if this canonical probability-based explanation can really account for the empirical success of deep learning. To resolve this issue, we propose an alternative utility-based explanation to the standard supervised learning procedure in deep learning. The basic idea is to interpret the learned neural network not as a probability model but as an ordinal utility function that encodes the preference revealed in training data. In this perspective, training of the neural network corresponds to a utility learning process. Specifically, we show that for all neural networks with softmax outputs, the SGD learning dynamic of maximum likelihood estimation (MLE) can be seen as an iteration process that optimizes the neural network toward an optimal utility function. This utility-based interpretation can explain several otherwise-paradoxical observations about the neural networks thus trained. Moreover, our utility-based theory also entails an equation that can transform the learned utility values back to a new kind of probability estimation with which probability-compatible decision rules enjoy dramatic (double-digits) performance improvements. These evidences collectively reveal a phenomenon of utility-probability duality in terms of what modern neural networks are (truly) modeling: We thought they are one thing (probabilities), until the unexplainable showed up; changing mindset and treating them as another thing (utility values) largely reconcile the theory, despite remaining subtleties regarding its original (probabilistic) identity.

We consider a sequential decision making problem where the agent faces the environment characterized by the stochastic discrete events and seeks an optimal intervention policy such that its long-term reward is maximized. This problem exists ubiquitously in social media, finance and health informatics but is rarely investigated by the conventional research in reinforcement learning. To this end, we present a novel framework of the model-based reinforcement learning where the agent's actions and observations are asynchronous stochastic discrete events occurring in continuous-time. We model the dynamics of the environment by Hawkes process with external intervention control term and develop an algorithm to embed such process in the Bellman equation which guides the direction of the value gradient. We demonstrate the superiority of our method in both synthetic simulator and real-world problem.

Kahneman & Tversky's prospect theory tells us that humans perceive random variables in a biased but well-defined manner; for example, humans are famously loss-averse. We show that objectives for aligning LLMs with human feedback implicitly incorporate many of these biases -- the success of these objectives (e.g., DPO) over cross-entropy minimization can partly be ascribed to them being human-aware loss functions (HALOs). However, the utility functions these methods attribute to humans still differ from those in the prospect theory literature. Using a Kahneman-Tversky model of human utility, we propose a HALO that directly maximizes the utility of generations instead of maximizing the log-likelihood of preferences, as current methods do. We call this approach Kahneman-Tversky Optimization (KTO), and it matches or exceeds the performance of preference-based methods at scales from 1B to 30B. Crucially, KTO does not need preferences -- only a binary signal of whether an output is desirable or undesirable for a given input. This makes it far easier to use in the real world, where preference data is scarce and expensive.

We consider algorithms for learning reward functions from human preferences over pairs of trajectory segments, as used in reinforcement learning from human feedback (RLHF). Most recent work assumes that human preferences are generated based only upon the reward accrued within those segments, or their partial return. Recent work casts doubt on the validity of this assumption, proposing an alternative preference model based upon regret. We investigate the consequences of assuming preferences are based upon partial return when they actually arise from regret. We argue that the learned function is an approximation of the optimal advantage function, A^*_r, not a reward function. We find that if a specific pitfall is addressed, this incorrect assumption is not particularly harmful, resulting in a highly shaped reward function. Nonetheless, this incorrect usage of A^*_r is less desirable than the appropriate and simpler approach of greedy maximization of A^*_r. From the perspective of the regret preference model, we also provide a clearer interpretation of fine tuning contemporary large language models with RLHF. This paper overall provides insight regarding why learning under the partial return preference model tends to work so well in practice, despite it conforming poorly to how humans give preferences.

We study distributionally robust expected values under optimal transport distance with a quadratic cost function. In general the duality method, for this computation for the payoff function f, requires the computation of the λc-transform f^{λc}. We show that under the quadratic cost function there exists an intuitive and easily implementable representation of f^{λc}, if f is convex and piecewise linear. We apply this to the robust expected shortfall under the risk-neutral measure of an unhedged call option, from the point of view of the writer, as well as that of a portfolio mixing underlying shares with a call and a put option.

In Reinforcement Learning (RL), an agent acts in an unknown environment to maximize the expected cumulative discounted sum of an external reward signal, i.e., the expected return. In practice, in many tasks of interest, such as policy optimization, the agent usually spends its interaction budget by collecting episodes of fixed length within a simulator (i.e., Monte Carlo simulation). However, given the discounted nature of the RL objective, this data collection strategy might not be the best option. Indeed, the rewards taken in early simulation steps weigh exponentially more than future rewards. Taking a cue from this intuition, in this paper, we design an a-priori budget allocation strategy that leads to the collection of trajectories of different lengths, i.e., truncated. The proposed approach provably minimizes the width of the confidence intervals around the empirical estimates of the expected return of a policy. After discussing the theoretical properties of our method, we make use of our trajectory truncation mechanism to extend Policy Optimization via Importance Sampling (POIS, Metelli et al., 2018) algorithm. Finally, we conduct a numerical comparison between our algorithm and POIS: the results are consistent with our theory and show that an appropriate truncation of the trajectories can succeed in improving performance.

We present a Spades bidding algorithm that is superior to recreational human players and to publicly available bots. Like in Bridge, the game of Spades is composed of two independent phases, bidding and playing. This paper focuses on the bidding algorithm, since this phase holds a precise challenge: based on the input, choose the bid that maximizes the agent's winning probability. Our Bidding-in-Spades (BIS) algorithm heuristically determines the bidding strategy by comparing the expected utility of each possible bid. A major challenge is how to estimate these expected utilities. To this end, we propose a set of domain-specific heuristics, and then correct them via machine learning using data from real-world players. The \BIS algorithm we present can be attached to any playing algorithm. It beats rule-based bidding bots when all use the same playing component. When combined with a rule-based playing algorithm, it is superior to the average recreational human.

Prospect Theory (PT) models human decision-making behaviour under uncertainty, among which linguistic uncertainty is commonly adopted in real-world scenarios. Although recent studies have developed some frameworks to test PT parameters for Large Language Models (LLMs), few have considered the fitness of PT itself on LLMs. Moreover, whether PT is robust under linguistic uncertainty perturbations, especially epistemic markers (e.g. "likely"), remains highly under-explored. To address these gaps, we design a three-stage workflow based on a classic behavioural economics experimental setup. We first estimate PT parameters with economics questions and evaluate PT's fitness with performance metrics. We then derive probability mappings for epistemic markers in the same context, and inject these mappings into the prompt to investigate the stability of PT parameters. Our findings suggest that modelling LLMs' decision-making with PT is not consistently reliable across models, and applying Prospect Theory to LLMs is likely not robust to epistemic uncertainty. The findings caution against the deployment of PT-based frameworks in real-world applications where epistemic ambiguity is prevalent, giving valuable insights in behaviour interpretation and future alignment direction for LLM decision-making.

We present a general convergent class of reinforcement learning algorithms that is founded on two distinct principles: (1) mapping value estimates to a different space using arbitrary functions from a broad class, and (2) linearly decomposing the reward signal into multiple channels. The first principle enables incorporating specific properties into the value estimator that can enhance learning. The second principle, on the other hand, allows for the value function to be represented as a composition of multiple utility functions. This can be leveraged for various purposes, e.g. dealing with highly varying reward scales, incorporating a priori knowledge about the sources of reward, and ensemble learning. Combining the two principles yields a general blueprint for instantiating convergent algorithms by orchestrating diverse mapping functions over multiple reward channels. This blueprint generalizes and subsumes algorithms such as Q-Learning, Log Q-Learning, and Q-Decomposition. In addition, our convergence proof for this general class relaxes certain required assumptions in some of these algorithms. Based on our theory, we discuss several interesting configurations as special cases. Finally, to illustrate the potential of the design space that our theory opens up, we instantiate a particular algorithm and evaluate its performance on the Atari suite.

We propose a reinforcement learning (RL) framework under a broad class of risk objectives, characterized by convex scoring functions. This class covers many common risk measures, such as variance, Expected Shortfall, entropic Value-at-Risk, and mean-risk utility. To resolve the time-inconsistency issue, we consider an augmented state space and an auxiliary variable and recast the problem as a two-state optimization problem. We propose a customized Actor-Critic algorithm and establish some theoretical approximation guarantees. A key theoretical contribution is that our results do not require the Markov decision process to be continuous. Additionally, we propose an auxiliary variable sampling method inspired by the alternating minimization algorithm, which is convergent under certain conditions. We validate our approach in simulation experiments with a financial application in statistical arbitrage trading, demonstrating the effectiveness of the algorithm.

Reinforcement learning from human feedback (RLHF) is bottlenecked by reward hacking, where the policy exploits errors in a proxy reward model (RM) and produces high RM scores without genuine quality gains. A natural mitigation is pessimism: lowering rewards in regions where the RM is uncertain. However, standard scalar RMs provide no principled notion of uncertainty. We argue that the right object is a distributional reward model p(rmid x,y). Under either a Bayesian inference or a KL-distributionally robust optimization (KL-DRO) lens, the KL-regularized RLHF objective admits a closed-form effective reward tilde r(x,y) = pmβlogE_p[e^{pm r/β}]. The pessimistic branch unifies the prior heuristics for RM ensemble aggregation: mean aggregation, worst-case optimization (WCO), and uncertainty-weighted optimization (UWO) all emerge as limits or truncations of this single expression. This also clarifies the implicit assumptions of each existing rule.

There is a strong link between the general concept of intelligence and the ability to collect and use information. The theory of Bayes-adaptive exploration offers an attractive optimality framework for training machines to perform complex information gathering tasks. However, the computational complexity of the resulting optimal control problem has limited the diffusion of the theory to mainstream deep AI research. In this paper we exploit the inherent mathematical structure of Bayes-adaptive problems in order to dramatically simplify the problem by making the reward structure denser while simultaneously decoupling the learning of exploitation and exploration policies. The key to this simplification comes from the novel concept of cross-value (i.e. the value of being in an environment while acting optimally according to another), which we use to quantify the value of currently available information. This results in a new denser reward structure that "cashes in" all future rewards that can be predicted from the current information state. In a set of experiments we show that the approach makes it possible to learn challenging information gathering tasks without the use of shaping and heuristic bonuses in situations where the standard RL algorithms fail.

You are a robot and you live in a Markov decision process (MDP) with a finite or an infinite number of transitions from state-action to next states. You got brains and so you plan before you act. Luckily, your roboparents equipped you with a generative model to do some Monte-Carlo planning. The world is waiting for you and you have no time to waste. You want your planning to be efficient. Sample-efficient. Indeed, you want to exploit the possible structure of the MDP by exploring only a subset of states reachable by following near-optimal policies. You want guarantees on sample complexity that depend on a measure of the quantity of near-optimal states. You want something, that is an extension of Monte-Carlo sampling (for estimating an expectation) to problems that alternate maximization (over actions) and expectation (over next states). But you do not want to StOP with exponential running time, you want something simple to implement and computationally efficient. You want it all and you want it now. You want TrailBlazer.

The prevalent deployment of learning from human preferences through reinforcement learning (RLHF) relies on two important approximations: the first assumes that pairwise preferences can be substituted with pointwise rewards. The second assumes that a reward model trained on these pointwise rewards can generalize from collected data to out-of-distribution data sampled by the policy. Recently, Direct Preference Optimisation (DPO) has been proposed as an approach that bypasses the second approximation and learn directly a policy from collected data without the reward modelling stage. However, this method still heavily relies on the first approximation. In this paper we try to gain a deeper theoretical understanding of these practical algorithms. In particular we derive a new general objective called PsiPO for learning from human preferences that is expressed in terms of pairwise preferences and therefore bypasses both approximations. This new general objective allows us to perform an in-depth analysis of the behavior of RLHF and DPO (as special cases of PsiPO) and to identify their potential pitfalls. We then consider another special case for PsiPO by setting Psi simply to Identity, for which we can derive an efficient optimisation procedure, prove performance guarantees and demonstrate its empirical superiority to DPO on some illustrative examples.

When fine-tuning pre-trained Large Language Models (LLMs) to align with human values and intentions, maximizing the estimated reward can lead to superior performance, but it also introduces potential risks due to deviations from the reference model's intended behavior. Most existing methods typically introduce KL divergence to constrain deviations between the trained model and the reference model; however, this may not be sufficient in certain applications that require tight risk control. In this paper, we introduce Risk-aware Direct Preference Optimization (Ra-DPO), a novel approach that incorporates risk-awareness by employing a class of nested risk measures. This approach formulates a constrained risk-aware advantage function maximization problem and then converts the Bradley-Terry model into a token-level representation. The objective function maximizes the likelihood of the policy while suppressing the deviation between a trained model and the reference model using a sequential risk ratio, thereby enhancing the model's risk-awareness. Experimental results across three open-source datasets: IMDb Dataset, Anthropic HH Dataset, and AlpacaEval, demonstrate the proposed method's superior performance in balancing alignment performance and model drift. Our code is opensourced at https://github.com/zlj123-max/Ra-DPO.

In reinforcement learning an agent interacts with the environment by taking actions and observing the next state and reward. When sampled probabilistically, these state transitions, rewards, and actions can all induce randomness in the observed long-term return. Traditionally, reinforcement learning algorithms average over this randomness to estimate the value function. In this paper, we build on recent work advocating a distributional approach to reinforcement learning in which the distribution over returns is modeled explicitly instead of only estimating the mean. That is, we examine methods of learning the value distribution instead of the value function. We give results that close a number of gaps between the theoretical and algorithmic results given by Bellemare, Dabney, and Munos (2017). First, we extend existing results to the approximate distribution setting. Second, we present a novel distributional reinforcement learning algorithm consistent with our theoretical formulation. Finally, we evaluate this new algorithm on the Atari 2600 games, observing that it significantly outperforms many of the recent improvements on DQN, including the related distributional algorithm C51.

In this paper, we formalise order-robust optimisation as an instance of online learning minimising simple regret, and propose Vroom, a zero'th order optimisation algorithm capable of achieving vanishing regret in non-stationary environments, while recovering favorable rates under stochastic reward-generating processes. Our results are the first to target simple regret definitions in adversarial scenarios unveiling a challenge that has been rarely considered in prior work.

Minimum Bayes risk (MBR) decoding outputs the hypothesis with the highest expected utility over the model distribution for some utility function. It has been shown to improve accuracy over beam search in conditional language generation problems and especially neural machine translation, in both human and automatic evaluations. However, the standard sampling-based algorithm for MBR is substantially more computationally expensive than beam search, requiring a large number of samples as well as a quadratic number of calls to the utility function, limiting its applicability. We describe an algorithm for MBR which gradually grows the number of samples used to estimate the utility while pruning hypotheses that are unlikely to have the highest utility according to confidence estimates obtained with bootstrap sampling. Our method requires fewer samples and drastically reduces the number of calls to the utility function compared to standard MBR while being statistically indistinguishable in terms of accuracy. We demonstrate the effectiveness of our approach in experiments on three language pairs, using chrF++ and COMET as utility/evaluation metrics.

We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, market impact, liquidity constraints or risk limits using modern deep reinforcement machine learning methods. We discuss how standard reinforcement learning methods can be applied to non-linear reward structures, i.e. in our case convex risk measures. As a general contribution to the use of deep learning for stochastic processes, we also show that the set of constrained trading strategies used by our algorithm is large enough to ε-approximate any optimal solution. Our algorithm can be implemented efficiently even in high-dimensional situations using modern machine learning tools. Its structure does not depend on specific market dynamics, and generalizes across hedging instruments including the use of liquid derivatives. Its computational performance is largely invariant in the size of the portfolio as it depends mainly on the number of hedging instruments available. We illustrate our approach by showing the effect on hedging under transaction costs in a synthetic market driven by the Heston model, where we outperform the standard "complete market" solution.

We explore algorithms to select actions in the causal bandit setting where the learner can choose to intervene on a set of random variables related by a causal graph, and the learner sequentially chooses interventions and observes a sample from the interventional distribution. The learner's goal is to quickly find the intervention, among all interventions on observable variables, that maximizes the expectation of an outcome variable. We depart from previous literature by assuming no knowledge of the causal graph except that latent confounders between the outcome and its ancestors are not present. We first show that the unknown graph problem can be exponentially hard in the parents of the outcome. To remedy this, we adopt an additional additive assumption on the outcome which allows us to solve the problem by casting it as an additive combinatorial linear bandit problem with full-bandit feedback. We propose a novel action-elimination algorithm for this setting, show how to apply this algorithm to the causal bandit problem, provide sample complexity bounds, and empirically validate our findings on a suite of randomly generated causal models, effectively showing that one does not need to explicitly learn the parents of the outcome to identify the best intervention.

In multi-armed bandits, the most-explored arms are the most informative, while reward maximization typically pulls only the best arm. We study the tradeoff between identifying arm means accurately and accumulating reward, and present an algorithm with regret guarantees that interpolates between the two objectives. We provide both upper and lower bounds and validate empirically.

The optimized certainty equivalent (OCE) is a family of risk measures that cover important examples such as entropic risk, conditional value-at-risk and mean-variance models. In this paper, we propose a new episodic risk-sensitive reinforcement learning formulation based on tabular Markov decision processes with recursive OCEs. We design an efficient learning algorithm for this problem based on value iteration and upper confidence bound. We derive an upper bound on the regret of the proposed algorithm, and also establish a minimax lower bound. Our bounds show that the regret rate achieved by our proposed algorithm has optimal dependence on the number of episodes and the number of actions.

As AIs rapidly advance and become more agentic, the risk they pose is governed not only by their capabilities but increasingly by their propensities, including goals and values. Tracking the emergence of goals and values has proven a longstanding problem, and despite much interest over the years it remains unclear whether current AIs have meaningful values. We propose a solution to this problem, leveraging the framework of utility functions to study the internal coherence of AI preferences. Surprisingly, we find that independently-sampled preferences in current LLMs exhibit high degrees of structural coherence, and moreover that this emerges with scale. These findings suggest that value systems emerge in LLMs in a meaningful sense, a finding with broad implications. To study these emergent value systems, we propose utility engineering as a research agenda, comprising both the analysis and control of AI utilities. We uncover problematic and often shocking values in LLM assistants despite existing control measures. These include cases where AIs value themselves over humans and are anti-aligned with specific individuals. To constrain these emergent value systems, we propose methods of utility control. As a case study, we show how aligning utilities with a citizen assembly reduces political biases and generalizes to new scenarios. Whether we like it or not, value systems have already emerged in AIs, and much work remains to fully understand and control these emergent representations.

A growing trend for value-based reinforcement learning (RL) algorithms is to capture more information than scalar value functions in the value network. One of the most well-known methods in this branch is distributional RL, which models return distribution instead of scalar value. In another line of work, hybrid reward architectures (HRA) in RL have studied to model source-specific value functions for each source of reward, which is also shown to be beneficial in performance. To fully inherit the benefits of distributional RL and hybrid reward architectures, we introduce Multi-Dimensional Distributional DQN (MD3QN), which extends distributional RL to model the joint return distribution from multiple reward sources. As a by-product of joint distribution modeling, MD3QN can capture not only the randomness in returns for each source of reward, but also the rich reward correlation between the randomness of different sources. We prove the convergence for the joint distributional Bellman operator and build our empirical algorithm by minimizing the Maximum Mean Discrepancy between joint return distribution and its Bellman target. In experiments, our method accurately models the joint return distribution in environments with richly correlated reward functions, and outperforms previous RL methods utilizing multi-dimensional reward functions in the control setting.

Simulation-based optimization is a widely used method to solve stochastic optimization problems. This method aims to identify an optimal solution by maximizing the expected value of the objective function. However, due to its computational complexity, the function cannot be accurately evaluated directly, hence it is estimated through simulation. Exploiting the enhanced efficiency of Quantum Amplitude Estimation (QAE) compared to classical Monte Carlo simulation, it frequently outpaces classical simulation-based optimization, resulting in notable performance enhancements in various scenarios. In this work, we make use of a quantum-enhanced algorithm for simulation-based optimization and apply it to solve a variant of the classical Newsvendor problem which is known to be NP-hard. Such problems provide the building block for supply chain management, particularly in inventory management and procurement optimization under risks and uncertainty

The game show Lucky 13 differs from other television game shows in that contestants are required to place a bet on their own knowledge of trivia by selecting a range that contains the number of questions that they answered correctly. We present a model for this game show using binomial random variables and generate tables outlining the optimal range the player should select based on maximization of two different utility functions. After analyzing the decisions made by some actual contestants on this show, we present a numerical simulation for how many questions an average player is expected to answer correctly based on question categories observed for two sample contestants.

Recent advances in aligning Large Language Models with human preferences have benefited from larger reward models and better preference data. However, most of these methodologies rely on the accuracy of the reward model. The reward models used in Reinforcement Learning with Human Feedback (RLHF) are typically learned from small datasets using stochastic optimization algorithms, making them prone to high variability. We illustrate the inconsistencies between reward models empirically on numerous open-source datasets. We theoretically show that the fluctuation of the reward models can be detrimental to the alignment problem because the derived policies are more overfitted to the reward model and, hence, are riskier if the reward model itself is uncertain. We use concentration of measure to motivate an uncertainty-aware, conservative algorithm for policy optimization. We show that such policies are more risk-averse in the sense that they are more cautious of uncertain rewards. We theoretically prove that our proposed methodology has less risk than the vanilla method. We corroborate our theoretical results with experiments based on designing an ensemble of reward models. We use this ensemble of reward models to align a language model using our methodology and observe that our empirical findings match our theoretical predictions.

In machine learning, the notion of multi-armed bandits refers to a class of online learning problems, in which an agent is supposed to simultaneously explore and exploit a given set of choice alternatives in the course of a sequential decision process. In the standard setting, the agent learns from stochastic feedback in the form of real-valued rewards. In many applications, however, numerical reward signals are not readily available -- instead, only weaker information is provided, in particular relative preferences in the form of qualitative comparisons between pairs of alternatives. This observation has motivated the study of variants of the multi-armed bandit problem, in which more general representations are used both for the type of feedback to learn from and the target of prediction. The aim of this paper is to provide a survey of the state of the art in this field, referred to as preference-based multi-armed bandits or dueling bandits. To this end, we provide an overview of problems that have been considered in the literature as well as methods for tackling them. Our taxonomy is mainly based on the assumptions made by these methods about the data-generating process and, related to this, the properties of the preference-based feedback.

This research presents a framework for quantitative risk management in volatile markets, specifically focusing on expectile-based methodologies applied to the FTSE 100 index. Traditional risk measures such as Value-at-Risk (VaR) have demonstrated significant limitations during periods of market stress, as evidenced during the 2008 financial crisis and subsequent volatile periods. This study develops an advanced expectile-based framework that addresses the shortcomings of conventional quantile-based approaches by providing greater sensitivity to tail losses and improved stability in extreme market conditions. The research employs a dataset spanning two decades of FTSE 100 returns, incorporating periods of high volatility, market crashes, and recovery phases. Our methodology introduces novel mathematical formulations for expectile regression models, enhanced threshold determination techniques using time series analysis, and robust backtesting procedures. The empirical results demonstrate that expectile-based Value-at-Risk (EVaR) consistently outperforms traditional VaR measures across various confidence levels and market conditions. The framework exhibits superior performance during volatile periods, with reduced model risk and enhanced predictive accuracy. Furthermore, the study establishes practical implementation guidelines for financial institutions and provides evidence-based recommendations for regulatory compliance and portfolio management. The findings contribute significantly to the literature on financial risk management and offer practical tools for practitioners dealing with volatile market environments.

Portfolio optimization has been a broad and intense area of interest for quantitative and statistical finance researchers and financial analysts. It is a challenging task to design a portfolio of stocks to arrive at the optimized values of the return and risk. This paper presents an algorithmic approach for designing optimum risk and eigen portfolios for five thematic sectors of the NSE of India. The prices of the stocks are extracted from the web from Jan 1, 2016, to Dec 31, 2020. Optimum risk and eigen portfolios for each sector are designed based on ten critical stocks from the sector. An LSTM model is designed for predicting future stock prices. Seven months after the portfolios were formed, on Aug 3, 2021, the actual returns of the portfolios are compared with the LSTM-predicted returns. The predicted and the actual returns indicate a very high-level accuracy of the LSTM model.

In this paper, we study risk-sensitive Reinforcement Learning (RL), focusing on the objective of Conditional Value at Risk (CVaR) with risk tolerance tau. Starting with multi-arm bandits (MABs), we show the minimax CVaR regret rate is Omega(tau^{-1AK}), where A is the number of actions and K is the number of episodes, and that it is achieved by an Upper Confidence Bound algorithm with a novel Bernstein bonus. For online RL in tabular Markov Decision Processes (MDPs), we show a minimax regret lower bound of Omega(tau^{-1SAK}) (with normalized cumulative rewards), where S is the number of states, and we propose a novel bonus-driven Value Iteration procedure. We show that our algorithm achieves the optimal regret of widetilde O(tau^{-1SAK}) under a continuity assumption and in general attains a near-optimal regret of widetilde O(tau^{-1}SAK), which is minimax-optimal for constant tau. This improves on the best available bounds. By discretizing rewards appropriately, our algorithms are computationally efficient.

In order to solve a task using reinforcement learning, it is necessary to first formalise the goal of that task as a reward function. However, for many real-world tasks, it is very difficult to manually specify a reward function that never incentivises undesirable behaviour. As a result, it is increasingly popular to use reward learning algorithms, which attempt to learn a reward function from data. However, the theoretical foundations of reward learning are not yet well-developed. In particular, it is typically not known when a given reward learning algorithm with high probability will learn a reward function that is safe to optimise. This means that reward learning algorithms generally must be evaluated empirically, which is expensive, and that their failure modes are difficult to anticipate in advance. One of the roadblocks to deriving better theoretical guarantees is the lack of good methods for quantifying the difference between reward functions. In this paper we provide a solution to this problem, in the form of a class of pseudometrics on the space of all reward functions that we call STARC (STAndardised Reward Comparison) metrics. We show that STARC metrics induce both an upper and a lower bound on worst-case regret, which implies that our metrics are tight, and that any metric with the same properties must be bilipschitz equivalent to ours. Moreover, we also identify a number of issues with reward metrics proposed by earlier works. Finally, we evaluate our metrics empirically, to demonstrate their practical efficacy. STARC metrics can be used to make both theoretical and empirical analysis of reward learning algorithms both easier and more principled.

We introduce a novel framework for simulating macroeconomic expectation formation using Large Language Model-Empowered Agents (LLM Agents). By constructing thousands of LLM Agents equipped with modules for personal characteristics, prior expectations, and knowledge, we replicate a survey experiment involving households and experts on inflation and unemployment. Our results show that although the expectations and thoughts generated by LLM Agents are more homogeneous than those of human participants, they still effectively capture key heterogeneity across agents and the underlying drivers of expectation formation. Furthermore, a module-ablation exercise highlights the critical role of prior expectations in simulating such heterogeneity. This approach complements traditional survey methods and offers new insights into AI behavioral science in macroeconomic research.

This paper investigates the problem of ensembling multiple strategies for sequential portfolios to outperform individual strategies in terms of long-term wealth. Due to the uncertainty of strategies' performances in the future market, which are often based on specific models and statistical assumptions, investors often mitigate risk and enhance robustness by combining multiple strategies, akin to common approaches in collective learning prediction. However, the absence of a distribution-free and consistent preference framework complicates decisions of combination due to the ambiguous objective. To address this gap, we introduce a novel framework for decision-making in combining strategies, irrespective of market conditions, by establishing the investor's preference between decisions and then forming a clear objective. Through this framework, we propose a combinatorial strategy construction, free from statistical assumptions, for any scale of component strategies, even infinite, such that it meets the determined criterion. Finally, we test the proposed strategy along with its accelerated variant and some other multi-strategies. The numerical experiments show results in favor of the proposed strategies, albeit with small tradeoffs in their Sharpe ratios, in which their cumulative wealths eventually exceed those of the best component strategies while the accelerated strategy significantly improves performance.

Major Internet advertising platforms offer budget pacing tools as a standard service for advertisers to manage their ad campaigns. Given the inherent non-stationarity in an advertiser's value and also competing advertisers' values over time, a commonly used approach is to learn a target expenditure plan that specifies a target spend as a function of time, and then run a controller that tracks this plan. This raises the question: how many historical samples are required to learn a good expenditure plan? We study this question by considering an advertiser repeatedly participating in T second-price auctions, where the tuple of her value and the highest competing bid is drawn from an unknown time-varying distribution. The advertiser seeks to maximize her total utility subject to her budget constraint. Prior work has shown the sufficiency of Tlog T samples per distribution to achieve the optimal O(T)-regret. We dramatically improve this state-of-the-art and show that just one sample per distribution is enough to achieve the near-optimal tilde O(T)-regret, while still being robust to noise in the sampling distributions.

In nonstationary bandit learning problems, the decision-maker must continually gather information and adapt their action selection as the latent state of the environment evolves. In each time period, some latent optimal action maximizes expected reward under the environment state. We view the optimal action sequence as a stochastic process, and take an information-theoretic approach to analyze attainable performance. We bound limiting per-period regret in terms of the entropy rate of the optimal action process. The bound applies to a wide array of problems studied in the literature and reflects the problem's information structure through its information-ratio.

We address the problem of optimizing a Brownian motion. We consider a (random) realization W of a Brownian motion with input space in [0,1]. Given W, our goal is to return an ε-approximation of its maximum using the smallest possible number of function evaluations, the sample complexity of the algorithm. We provide an algorithm with sample complexity of order log^2(1/ε). This improves over previous results of Al-Mharmah and Calvin (1996) and Calvin et al. (2017) which provided only polynomial rates. Our algorithm is adaptive---each query depends on previous values---and is an instance of the optimism-in-the-face-of-uncertainty principle.

Portfolio Selection is an important real-world financial task and has attracted extensive attention in artificial intelligence communities. This task, however, has two main difficulties: (i) the non-stationary price series and complex asset correlations make the learning of feature representation very hard; (ii) the practicality principle in financial markets requires controlling both transaction and risk costs. Most existing methods adopt handcraft features and/or consider no constraints for the costs, which may make them perform unsatisfactorily and fail to control both costs in practice. In this paper, we propose a cost-sensitive portfolio selection method with deep reinforcement learning. Specifically, a novel two-stream portfolio policy network is devised to extract both price series patterns and asset correlations, while a new cost-sensitive reward function is developed to maximize the accumulated return and constrain both costs via reinforcement learning. We theoretically analyze the near-optimality of the proposed reward, which shows that the growth rate of the policy regarding this reward function can approach the theoretical optimum. We also empirically evaluate the proposed method on real-world datasets. Promising results demonstrate the effectiveness and superiority of the proposed method in terms of profitability, cost-sensitivity and representation abilities.

Risk-sensitive reinforcement learning (RL) has become a popular tool to control the risk of uncertain outcomes and ensure reliable performance in various sequential decision-making problems. While policy gradient methods have been developed for risk-sensitive RL, it remains unclear if these methods enjoy the same global convergence guarantees as in the risk-neutral case. In this paper, we consider a class of dynamic time-consistent risk measures, called Expected Conditional Risk Measures (ECRMs), and derive policy gradient updates for ECRM-based objective functions. Under both constrained direct parameterization and unconstrained softmax parameterization, we provide global convergence and iteration complexities of the corresponding risk-averse policy gradient algorithms. We further test risk-averse variants of REINFORCE and actor-critic algorithms to demonstrate the efficacy of our method and the importance of risk control.

Large Language Models (LLMs) can produce surprisingly sophisticated estimates of their own uncertainty. However, it remains unclear to what extent this expressed confidence is tied to the reasoning, knowledge, or decision making of the model. To test this, we introduce RiskEval: a framework designed to evaluate whether models adjust their abstention policies in response to varying error penalties. Our evaluation of several frontier models reveals a critical dissociation: models are neither cost-aware when articulating their verbal confidence, nor strategically responsive when deciding whether to engage or abstain under high-penalty conditions. Even when extreme penalties render frequent abstention the mathematically optimal strategy, models almost never abstain, resulting in utility collapse. This indicates that calibrated verbal confidence scores may not be sufficient to create trustworthy and interpretable AI systems, as current models lack the strategic agency to convert uncertainty signals into optimal and risk-sensitive decisions.

Designing an optimum portfolio for allocating suitable weights to its constituent assets so that the return and risk associated with the portfolio are optimized is a computationally hard problem. The seminal work of Markowitz that attempted to solve the problem by estimating the future returns of the stocks is found to perform sub-optimally on real-world stock market data. This is because the estimation task becomes extremely challenging due to the stochastic and volatile nature of stock prices. This work illustrates three approaches to portfolio design minimizing the risk, optimizing the risk, and assigning equal weights to the stocks of a portfolio. Thirteen critical sectors listed on the National Stock Exchange (NSE) of India are first chosen. Three portfolios are designed following the above approaches choosing the top ten stocks from each sector based on their free-float market capitalization. The portfolios are designed using the historical prices of the stocks from Jan 1, 2017, to Dec 31, 2022. The portfolios are evaluated on the stock price data from Jan 1, 2022, to Dec 31, 2022. The performances of the portfolios are compared, and the portfolio yielding the higher return for each sector is identified.

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al.(2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has mathcal{O}(H^3S^2A/varepsilon^2) sample complexity thus improving the varepsilon-dependence upon existing results, where S is a number of states, A is a number of actions, H is an episode length, and varepsilon is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order mathcal{O}(poly(S,A,H)/varepsilon). Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to mathcal{O}(H^2SA/varepsilon^2), yielding a statistical separation between maximum entropy exploration and reward-free exploration.

Active inference offers a first principle account of sentient behaviour, from which special and important cases can be derived, e.g., reinforcement learning, active learning, Bayes optimal inference, Bayes optimal design, etc. Active inference resolves the exploitation-exploration dilemma in relation to prior preferences, by placing information gain on the same footing as reward or value. In brief, active inference replaces value functions with functionals of (Bayesian) beliefs, in the form of an expected (variational) free energy. In this paper, we consider a sophisticated kind of active inference, using a recursive form of expected free energy. Sophistication describes the degree to which an agent has beliefs about beliefs. We consider agents with beliefs about the counterfactual consequences of action for states of affairs and beliefs about those latent states. In other words, we move from simply considering beliefs about 'what would happen if I did that' to 'what would I believe about what would happen if I did that'. The recursive form of the free energy functional effectively implements a deep tree search over actions and outcomes in the future. Crucially, this search is over sequences of belief states, as opposed to states per se. We illustrate the competence of this scheme, using numerical simulations of deep decision problems.

Large Language Model (LLM) agents deployed for real-world tasks face a fundamental dilemma: user requests are underspecified, yet agents must decide whether to act on incomplete information or interrupt users for clarification. Existing approaches either rely on brittle confidence thresholds that require task-specific tuning, or fail to account for the varying stakes of different decisions. We introduce a decision-theoretic framework that resolves this trade-off through the Value of Information (VoI), enabling agents to dynamically weigh the expected utility gain from asking questions against the cognitive cost imposed on users. Our inference-time method requires no hyperparameter tuning and adapts seamlessly across contexts-from casual games to medical diagnosis. Experiments across four diverse domains (20 Questions, medical diagnosis, flight booking, and e-commerce) show that VoI consistently matches or exceeds the best manually-tuned baselines, achieving up to 1.36 utility points higher in high-cost settings. This work provides a parameter-free framework for adaptive agent communication that explicitly balances task risk, query ambiguity, and user effort.

Reinforcement learning with verifiable reward has recently emerged as a central paradigm for post-training large language models (LLMs); however, prevailing mean-based methods, such as Group Relative Policy Optimization (GRPO), suffer from entropy collapse and limited reasoning gains. We argue that these issues stem from overemphasizing high-probability output sequences while neglecting rare but informative reasoning paths. To address these challenges, we propose Risk-based Policy Optimization (RiskPO), which substitutes classical mean-based objectives with principled risk measures. Specifically, we introduce a Mixed Value-at-Risk objective that integrates weighted attention over multiple regions of the reward distribution, thereby amplifying gradient signals on challenging instances and preventing overconfident convergence. We further design a bundling scheme that aggregates multiple questions into bundles, thus enriching the feedback signal and yielding more stable and informative training dynamics. Theoretically, we prove that the risk-averse update alleviates entropy collapse and promotes exploration. Numerically, RiskPO achieves consistent and significant improvements in mathematical reasoning, multi-modal reasoning, and code generation benchmarks, surpassing GRPO and its variants on both Pass@1 and Pass@k metrics. Our results demonstrate that risk-based optimization provides a rigorous and effective paradigm for enhancing LLM reasoning capabilities.

The prevalence and importance of algorithmic two-sided marketplaces has drawn attention to the issue of fairness in such settings. Algorithmic decisions are used in assigning students to schools, users to advertisers, and applicants to job interviews. These decisions should heed the preferences of individuals, and simultaneously be fair with respect to their merits (synonymous with fit, future performance, or need). Merits conditioned on observable features are always uncertain, a fact that is exacerbated by the widespread use of machine learning algorithms to infer merit from the observables. As our key contribution, we carefully axiomatize a notion of individual fairness in the two-sided marketplace setting which respects the uncertainty in the merits; indeed, it simultaneously recognizes uncertainty as the primary potential cause of unfairness and an approach to address it. We design a linear programming framework to find fair utility-maximizing distributions over allocations, and we show that the linear program is robust to perturbations in the estimated parameters of the uncertain merit distributions, a key property in combining the approach with machine learning techniques.

In order for agents in multi-agent systems (MAS) to be safe, they need to take into account the risks posed by the actions of other agents. However, the dominant paradigm in game theory (GT) assumes that agents are not affected by risk from other agents and only strive to maximise their expected utility. For example, in hybrid human-AI driving systems, it is necessary to limit large deviations in reward resulting from car crashes. Although there are equilibrium concepts in game theory that take into account risk aversion, they either assume that agents are risk-neutral with respect to the uncertainty caused by the actions of other agents, or they are not guaranteed to exist. We introduce a new GT-based Risk-Averse Equilibrium (RAE) that always produces a solution that minimises the potential variance in reward accounting for the strategy of other agents. Theoretically and empirically, we show RAE shares many properties with a Nash Equilibrium (NE), establishing convergence properties and generalising to risk-dominant NE in certain cases. To tackle large-scale problems, we extend RAE to the PSRO multi-agent reinforcement learning (MARL) framework. We empirically demonstrate the minimum reward variance benefits of RAE in matrix games with high-risk outcomes. Results on MARL experiments show RAE generalises to risk-dominant NE in a trust dilemma game and that it reduces instances of crashing by 7x in an autonomous driving setting versus the best performing baseline.

Online allocation problems with resource constraints are central problems in revenue management and online advertising. In these problems, requests arrive sequentially during a finite horizon and, for each request, a decision maker needs to choose an action that consumes a certain amount of resources and generates reward. The objective is to maximize cumulative rewards subject to a constraint on the total consumption of resources. In this paper, we consider a data-driven setting in which the reward and resource consumption of each request are generated using an input model that is unknown to the decision maker. We design a general class of algorithms that attain good performance in various input models without knowing which type of input they are facing. In particular, our algorithms are asymptotically optimal under independent and identically distributed inputs as well as various non-stationary stochastic input models, and they attain an asymptotically optimal fixed competitive ratio when the input is adversarial. Our algorithms operate in the Lagrangian dual space: they maintain a dual multiplier for each resource that is updated using online mirror descent. By choosing the reference function accordingly, we recover the dual sub-gradient descent and dual multiplicative weights update algorithm. The resulting algorithms are simple, fast, and do not require convexity in the revenue function, consumption function and action space, in contrast to existing methods for online allocation problems. We discuss applications to network revenue management, online bidding in repeated auctions with budget constraints, online proportional matching with high entropy, and personalized assortment optimization with limited inventory.

In many areas of medicine, security, and life sciences, we want to allocate limited resources to different sources in order to detect extreme values. In this paper, we study an efficient way to allocate these resources sequentially under limited feedback. While sequential design of experiments is well studied in bandit theory, the most commonly optimized property is the regret with respect to the maximum mean reward. However, in other problems such as network intrusion detection, we are interested in detecting the most extreme value output by the sources. Therefore, in our work we study extreme regret which measures the efficiency of an algorithm compared to the oracle policy selecting the source with the heaviest tail. We propose the ExtremeHunter algorithm, provide its analysis, and evaluate it empirically on synthetic and real-world experiments.

Methods for controlling large language models (LLMs), including local weight fine-tuning, LoRA-based adaptation, and activation-based interventions, are often studied in isolation, obscuring their connections and making comparison difficult. In this work, we present a unified view that frames these interventions as dynamic weight updates induced by a control signal, placing them within a single conceptual framework. Building on this view, we propose a unified preference-utility analysis that separates control effects into preference, defined as the tendency toward a target concept, and utility, defined as coherent and task-valid generation, and measures both on a shared log-odds scale using polarity-paired contrastive examples. Across methods, we observe a consistent trade-off between preference and utility: stronger control increases preference while predictably reducing utility. We further explain this behavior through an activation manifold perspective, in which control shifts representations along target-concept directions to enhance preference, while utility declines primarily when interventions push representations off the model's valid-generation manifold. Finally, we introduce a new steering approach SPLIT guided by this analysis that improves preference while better preserving utility. Code is available at https://github.com/zjunlp/EasyEdit/blob/main/examples/SPLIT.md.

Unsupervised reinforcement learning aims at learning a generalist policy in a reward-free manner for fast adaptation to downstream tasks. Most of the existing methods propose to provide an intrinsic reward based on surprise. Maximizing or minimizing surprise drives the agent to either explore or gain control over its environment. However, both strategies rely on a strong assumption: the entropy of the environment's dynamics is either high or low. This assumption may not always hold in real-world scenarios, where the entropy of the environment's dynamics may be unknown. Hence, choosing between the two objectives is a dilemma. We propose a novel yet simple mixture of policies to address this concern, allowing us to optimize an objective that simultaneously maximizes and minimizes the surprise. Concretely, we train one mixture component whose objective is to maximize the surprise and another whose objective is to minimize the surprise. Hence, our method does not make assumptions about the entropy of the environment's dynamics. We call our method a Mixture Of SurpriseS (MOSS) for unsupervised reinforcement learning. Experimental results show that our simple method achieves state-of-the-art performance on the URLB benchmark, outperforming previous pure surprise maximization-based objectives. Our code is available at: https://github.com/LeapLabTHU/MOSS.

Direct Alignment Algorithms (DAAs), such as Direct Preference Optimisation (DPO) and Identity Preference Optimisation (IPO), have emerged as alternatives to online Reinforcement Learning from Human Feedback (RLHF) algorithms such as Proximal Policy Optimisation (PPO) for aligning language models to human preferences, without the need for explicit reward modelling. These methods generally aim to increase the likelihood of generating better (preferred) completions while discouraging worse (non-preferred) ones, while staying close to the original model's behaviour. In this work, we explore the relationship between completion likelihood and model performance in state-of-the-art DAAs, and identify a critical issue of likelihood over-optimisation. Contrary to expectations, we find that higher likelihood of better completions and larger margins between better and worse completion likelihoods do not necessarily lead to better performance, and may even degrade it. Our analysis reveals that while higher likelihood correlates with better memorisation of factual knowledge patterns, a slightly lower completion likelihood tends to improve output diversity, thus leading to better generalisation to unseen scenarios. Moreover, we identify two key indicators that signal when over-optimised output diversity begins to harm performance: Decreasing Entropy over Top-k Tokens and Diminishing Top-k Probability Mass. Our experimental results validate that these indicators are reliable signs of declining performance under different regularisations, helping prevent over-optimisation and improve alignment with human preferences.

We consider a fair division model in which agents have positive, zero and negative utilities for items. For this model, we analyse one existing fairness property - EFX - and three new and related properties - EFX_0, EFX^3 and EF1^3 - in combination with Pareto-optimality. With general utilities, we give a modified version of an existing algorithm for computing an EF1^3 allocation. With -alpha/0/alpha utilities, this algorithm returns an EFX^3 and PO allocation. With absolute identical utilities, we give a new algorithm for an EFX and PO allocation. With -alpha/0/beta utilities, this algorithm also returns such an allocation. We report some new impossibility results as well.

We study the problem of fairly allocating indivisible goods among a set of agents. Our focus is on the existence of allocations that give each agent their maximin fair share--the value they are guaranteed if they divide the goods into as many bundles as there are agents, and receive their lowest valued bundle. An MMS allocation is one where every agent receives at least their maximin fair share. We examine the existence of such allocations when agents have cost utilities. In this setting, each item has an associated cost, and an agent's valuation for an item is the cost of the item if it is useful to them, and zero otherwise. Our main results indicate that cost utilities are a promising restriction for achieving MMS. We show that for the case of three agents with cost utilities, an MMS allocation always exists. We also show that when preferences are restricted slightly further--to what we call laminar set approvals--we can guarantee MMS allocations for any number of agents. Finally, we explore if it is possible to guarantee each agent their maximin fair share while using a strategyproof mechanism.

In this report, we survey Bayesian Optimization methods focussed on the Multi-Armed Bandit Problem. We take the help of the paper "Portfolio Allocation for Bayesian Optimization". We report a small literature survey on the acquisition functions and the types of portfolio strategies used in papers discussing Bayesian Optimization. We also replicate the experiments and report our findings and compare them to the results in the paper. Code link: https://colab.research.google.com/drive/1GZ14klEDoe3dcBeZKo5l8qqrKf_GmBDn?usp=sharing#scrollTo=XgIBau3O45_V.

Inverse reinforcement learning (IRL) aims to infer an agent's preferences (represented as a reward function R) from their behaviour (represented as a policy pi). To do this, we need a behavioural model of how pi relates to R. In the current literature, the most common behavioural models are optimality, Boltzmann-rationality, and causal entropy maximisation. However, the true relationship between a human's preferences and their behaviour is much more complex than any of these behavioural models. This means that the behavioural models are misspecified, which raises the concern that they may lead to systematic errors if applied to real data. In this paper, we analyse how sensitive the IRL problem is to misspecification of the behavioural model. Specifically, we provide necessary and sufficient conditions that completely characterise how the observed data may differ from the assumed behavioural model without incurring an error above a given threshold. In addition to this, we also characterise the conditions under which a behavioural model is robust to small perturbations of the observed policy, and we analyse how robust many behavioural models are to misspecification of their parameter values (such as e.g.\ the discount rate). Our analysis suggests that the IRL problem is highly sensitive to misspecification, in the sense that very mild misspecification can lead to very large errors in the inferred reward function.

Multi-armed bandits a simple but very powerful framework for algorithms that make decisions over time under uncertainty. An enormous body of work has accumulated over the years, covered in several books and surveys. This book provides a more introductory, textbook-like treatment of the subject. Each chapter tackles a particular line of work, providing a self-contained, teachable technical introduction and a brief review of the further developments; many of the chapters conclude with exercises. The book is structured as follows. The first four chapters are on IID rewards, from the basic model to impossibility results to Bayesian priors to Lipschitz rewards. The next three chapters cover adversarial rewards, from the full-feedback version to adversarial bandits to extensions with linear rewards and combinatorially structured actions. Chapter 8 is on contextual bandits, a middle ground between IID and adversarial bandits in which the change in reward distributions is completely explained by observable contexts. The last three chapters cover connections to economics, from learning in repeated games to bandits with supply/budget constraints to exploration in the presence of incentives. The appendix provides sufficient background on concentration and KL-divergence. The chapters on "bandits with similarity information", "bandits with knapsacks" and "bandits and agents" can also be consumed as standalone surveys on the respective topics.

In the last decade, Deep Reinforcement Learning has evolved into a powerful tool for complex sequential decision-making problems. It combines deep learning's proficiency in processing rich input signals with reinforcement learning's adaptability across diverse control tasks. At its core, an RL agent seeks to maximize its cumulative reward, enabling AI algorithms to uncover novel solutions previously unknown to experts. However, this focus on reward maximization also introduces a significant difficulty: improper reward specification can result in unexpected, misaligned agent behavior and inefficient learning. The complexity of accurately specifying the reward function is further amplified by the sequential nature of the task, the sparsity of learning signals, and the multifaceted aspects of the desired behavior. In this thesis, we survey the literature on effective reward specification strategies, identify core challenges relating to each of these approaches, and propose original contributions addressing the issue of sample efficiency and alignment in deep reinforcement learning. Reward specification represents one of the most challenging aspects of applying reinforcement learning in real-world domains. Our work underscores the absence of a universal solution to this complex and nuanced challenge; solving it requires selecting the most appropriate tools for the specific requirements of each unique application.

We present counterfactual planning as a design approach for creating a range of safety mechanisms that can be applied in hypothetical future AI systems which have Artificial General Intelligence. The key step in counterfactual planning is to use an AGI machine learning system to construct a counterfactual world model, designed to be different from the real world the system is in. A counterfactual planning agent determines the action that best maximizes expected utility in this counterfactual planning world, and then performs the same action in the real world. We use counterfactual planning to construct an AGI agent emergency stop button, and a safety interlock that will automatically stop the agent before it undergoes an intelligence explosion. We also construct an agent with an input terminal that can be used by humans to iteratively improve the agent's reward function, where the incentive for the agent to manipulate this improvement process is suppressed. As an example of counterfactual planning in a non-agent AGI system, we construct a counterfactual oracle. As a design approach, counterfactual planning is built around the use of a graphical notation for defining mathematical counterfactuals. This two-diagram notation also provides a compact and readable language for reasoning about the complex types of self-referencing and indirect representation which are typically present inside machine learning agents.

We consider the problem of finding an input to a stochastic black box function such that the scalar output of the black box function is as close as possible to a target value in the sense of the expected squared error. While the optimization of stochastic black boxes is classic in (robust) Bayesian optimization, the current approaches based on Gaussian processes predominantly focus either on i) maximization/minimization rather than target value optimization or ii) on the expectation, but not the variance of the output, ignoring output variations due to stochasticity in uncontrollable environmental variables. In this work, we fill this gap and derive acquisition functions for common criteria such as the expected improvement, the probability of improvement, and the lower confidence bound, assuming that aleatoric effects are Gaussian with known variance. Our experiments illustrate that this setting is compatible with certain extensions of Gaussian processes, and show that the thus derived acquisition functions can outperform classical Bayesian optimization even if the latter assumptions are violated. An industrial use case in billet forging is presented.

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses. In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of m adaptively chosen functions on an unknown distribution given n random samples. We show that, surprisingly, there is a way to estimate an exponential in n number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question.

In many real-world sequential decision-making problems, an action does not immediately reflect on the feedback and spreads its effects over a long time frame. For instance, in online advertising, investing in a platform produces an instantaneous increase of awareness, but the actual reward, i.e., a conversion, might occur far in the future. Furthermore, whether a conversion takes place depends on: how fast the awareness grows, its vanishing effects, and the synergy or interference with other advertising platforms. Previous work has investigated the Multi-Armed Bandit framework with the possibility of delayed and aggregated feedback, without a particular structure on how an action propagates in the future, disregarding possible dynamical effects. In this paper, we introduce a novel setting, the Dynamical Linear Bandits (DLB), an extension of the linear bandits characterized by a hidden state. When an action is performed, the learner observes a noisy reward whose mean is a linear function of the hidden state and of the action. Then, the hidden state evolves according to linear dynamics, affected by the performed action too. We start by introducing the setting, discussing the notion of optimal policy, and deriving an expected regret lower bound. Then, we provide an optimistic regret minimization algorithm, Dynamical Linear Upper Confidence Bound (DynLin-UCB), that suffers an expected regret of order mathcal{O} Big( d sqrt{T}{(1-rho)^{3/2}} Big), where rho is a measure of the stability of the system, and d is the dimension of the action vector. Finally, we conduct a numerical validation on a synthetic environment and on real-world data to show the effectiveness of DynLin-UCB in comparison with several baselines.

We study Pareto optimality in multi-objective multi-armed bandit by providing a formulation of adversarial multi-objective multi-armed bandit and defining its Pareto regrets that can be applied to both stochastic and adversarial settings. The regrets do not rely on any scalarization functions and reflect Pareto optimality compared to scalarized regrets. We also present new algorithms assuming both with and without prior information of the multi-objective multi-armed bandit setting. The algorithms are shown optimal in adversarial settings and nearly optimal up to a logarithmic factor in stochastic settings simultaneously by our established upper bounds and lower bounds on Pareto regrets. Moreover, the lower bound analyses show that the new regrets are consistent with the existing Pareto regret for stochastic settings and extend an adversarial attack mechanism from bandit to the multi-objective one.

In the stochastic multi-armed bandit problem, a randomized probability matching policy called Thompson sampling (TS) has shown excellent performance in various reward models. In addition to the empirical performance, TS has been shown to achieve asymptotic problem-dependent lower bounds in several models. However, its optimality has been mainly addressed under light-tailed or one-parameter models that belong to exponential families. In this paper, we consider the optimality of TS for the Pareto model that has a heavy tail and is parameterized by two unknown parameters. Specifically, we discuss the optimality of TS with probability matching priors that include the Jeffreys prior and the reference priors. We first prove that TS with certain probability matching priors can achieve the optimal regret bound. Then, we show the suboptimality of TS with other priors, including the Jeffreys and the reference priors. Nevertheless, we find that TS with the Jeffreys and reference priors can achieve the asymptotic lower bound if one uses a truncation procedure. These results suggest carefully choosing noninformative priors to avoid suboptimality and show the effectiveness of truncation procedures in TS-based policies.

Reinforcement learning from human feedback usually models preferences using a reward model that does not distinguish between people. We argue that this is unlikely to be a good design choice in contexts with high potential for disagreement, like in the training of large language models. We propose a method to specialise a reward model to a person or group of people. Our approach builds on the observation that individual preferences can be captured as a linear combination of a set of general reward features. We show how to learn such features and subsequently use them to quickly adapt the reward model to a specific individual, even if their preferences are not reflected in the training data. We present experiments with large language models comparing the proposed architecture with a non-adaptive reward model and also adaptive counterparts, including models that do in-context personalisation. Depending on how much disagreement there is in the training data, our model either significantly outperforms the baselines or matches their performance with a simpler architecture and more stable training.

This paper studies distributional model risk in marginal problems, where each marginal measure is assumed to lie in a Wasserstein ball centered at a fixed reference measure with a given radius. Theoretically, we establish several fundamental results including strong duality, finiteness of the proposed Wasserstein distributional model risk, and the existence of an optimizer at each radius. In addition, we show continuity of the Wasserstein distributional model risk as a function of the radius. Using strong duality, we extend the well-known Makarov bounds for the distribution function of the sum of two random variables with given marginals to Wasserstein distributionally robust Markarov bounds. Practically, we illustrate our results on four distinct applications when the sample information comes from multiple data sources and only some marginal reference measures are identified. They are: partial identification of treatment effects; externally valid treatment choice via robust welfare functions; Wasserstein distributionally robust estimation under data combination; and evaluation of the worst aggregate risk measures.

The relationship between material properties and independent variables such as temperature, external field or time, is usually represented by a curve or surface in a multi-dimensional space. Determining such a curve or surface requires a series of experiments or calculations which are often time and cost consuming. A general strategy uses an appropriate utility function to sample the space to recommend the next optimal experiment or calculation within an active learning loop. However, knowing what the optimal sampling strategy to use to minimize the number of experiments is an outstanding problem. We compare a number of strategies based on directed exploration on several materials problems of varying complexity using a Kriging based model. These include one dimensional curves such as the fatigue life curve for 304L stainless steel and the Liquidus line of the Fe-C phase diagram, surfaces such as the Hartmann 3 function in 3D space and the fitted intermolecular potential for Ar-SH, and a four dimensional data set of experimental measurements for BaTiO3 based ceramics. We also consider the effects of experimental noise on the Hartmann 3 function. We find that directed exploration guided by maximum variance provides better performance overall, converging faster across several data sets. However, for certain problems, the trade-off methods incorporating exploitation can perform at least as well, if not better than maximum variance. Thus, we discuss how the choice of the utility function depends on the distribution of the data, the model performance and uncertainties, additive noise as well as the budget.

To survive in dynamic and uncertain environments, individuals must develop effective decision strategies that balance information gathering and decision commitment. Models of such strategies often prioritize either optimizing tangible payoffs, like reward rate, or gathering information to support a diversity of (possibly unknown) objectives. However, our understanding of the relative merits of these two approaches remains incomplete, in part because direct comparisons have been limited to idealized, static environments that lack the dynamic complexity of the real world. Here we compared the performance of normative reward- and information-seeking strategies in a dynamic foraging task. Both strategies show similar transitions between exploratory and exploitative behaviors as environmental uncertainty changes. However, we find subtle disparities in the actions they take, resulting in meaningful performance differences: whereas reward-seeking strategies generate slightly more reward on average, information-seeking strategies provide more consistent and predictable outcomes. Our findings support the adaptive value of information-seeking behaviors that can mitigate risk with minimal reward loss.

The bandits with knapsack (BwK) framework models online decision-making problems in which an agent makes a sequence of decisions subject to resource consumption constraints. The traditional model assumes that each action consumes a non-negative amount of resources and the process ends when the initial budgets are fully depleted. We study a natural generalization of the BwK framework which allows non-monotonic resource utilization, i.e., resources can be replenished by a positive amount. We propose a best-of-both-worlds primal-dual template that can handle any online learning problem with replenishment for which a suitable primal regret minimizer exists. In particular, we provide the first positive results for the case of adversarial inputs by showing that our framework guarantees a constant competitive ratio alpha when B=Omega(T) or when the possible per-round replenishment is a positive constant. Moreover, under a stochastic input model, our algorithm yields an instance-independent O(T^{1/2}) regret bound which complements existing instance-dependent bounds for the same setting. Finally, we provide applications of our framework to some economic problems of practical relevance.

The utility of reinforcement learning is limited by the alignment of reward functions with the interests of human stakeholders. One promising method for alignment is to learn the reward function from human-generated preferences between pairs of trajectory segments, a type of reinforcement learning from human feedback (RLHF). These human preferences are typically assumed to be informed solely by partial return, the sum of rewards along each segment. We find this assumption to be flawed and propose modeling human preferences instead as informed by each segment's regret, a measure of a segment's deviation from optimal decision-making. Given infinitely many preferences generated according to regret, we prove that we can identify a reward function equivalent to the reward function that generated those preferences, and we prove that the previous partial return model lacks this identifiability property in multiple contexts. We empirically show that our proposed regret preference model outperforms the partial return preference model with finite training data in otherwise the same setting. Additionally, we find that our proposed regret preference model better predicts real human preferences and also learns reward functions from these preferences that lead to policies that are better human-aligned. Overall, this work establishes that the choice of preference model is impactful, and our proposed regret preference model provides an improvement upon a core assumption of recent research. We have open sourced our experimental code, the human preferences dataset we gathered, and our training and preference elicitation interfaces for gathering a such a dataset.

For continuous action spaces, actor-critic methods are widely used in online reinforcement learning (RL). However, unlike RL algorithms for discrete actions, which generally model the optimal value function using the Bellman optimality operator, RL algorithms for continuous actions typically model Q-values for the current policy using the Bellman operator. These algorithms for continuous actions rely exclusively on policy updates for improvement, which often results in low sample efficiency. This study examines the effectiveness of incorporating the Bellman optimality operator into actor-critic frameworks. Experiments in a simple environment show that modeling optimal values accelerates learning but leads to overestimation bias. To address this, we propose an annealing approach that gradually transitions from the Bellman optimality operator to the Bellman operator, thereby accelerating learning while mitigating bias. Our method, combined with TD3 and SAC, significantly outperforms existing approaches across various locomotion and manipulation tasks, demonstrating improved performance and robustness to hyperparameters related to optimality. The code for this study is available at https://github.com/motokiomura/annealed-q-learning.

Model-based deep reinforcement learning has achieved success in various domains that require high sample efficiencies, such as Go and robotics. However, there are some remaining issues, such as planning efficient explorations to learn more accurate dynamic models, evaluating the uncertainty of the learned models, and more rational utilization of models. To mitigate these issues, we present MEEE, a model-ensemble method that consists of optimistic exploration and weighted exploitation. During exploration, unlike prior methods directly selecting the optimal action that maximizes the expected accumulative return, our agent first generates a set of action candidates and then seeks out the optimal action that takes both expected return and future observation novelty into account. During exploitation, different discounted weights are assigned to imagined transition tuples according to their model uncertainty respectively, which will prevent model predictive error propagation in agent training. Experiments on several challenging continuous control benchmark tasks demonstrated that our approach outperforms other model-free and model-based state-of-the-art methods, especially in sample complexity.

We investigate stochastic combinatorial semi-bandits, where the entire joint distribution of outcomes impacts the complexity of the problem instance (unlike in the standard bandits). Typical distributions considered depend on specific parameter values, whose prior knowledge is required in theory but quite difficult to estimate in practice; an example is the commonly assumed sub-Gaussian family. We alleviate this issue by instead considering a new general family of sub-exponential distributions, which contains bounded and Gaussian ones. We prove a new lower bound on the expected regret on this family, that is parameterized by the unknown covariance matrix of outcomes, a tighter quantity than the sub-Gaussian matrix. We then construct an algorithm that uses covariance estimates, and provide a tight asymptotic analysis of the regret. Finally, we apply and extend our results to the family of sparse outcomes, which has applications in many recommender systems.

In recent years, significant attention has been directed towards learning average-reward Markov Decision Processes (MDPs). However, existing algorithms either suffer from sub-optimal regret guarantees or computational inefficiencies. In this paper, we present the first tractable algorithm with minimax optimal regret of mathrm{O}(mathrm{sp(h^*) S A T}), where sp(h^*) is the span of the optimal bias function h^*, S times A is the size of the state-action space and T the number of learning steps. Remarkably, our algorithm does not require prior information on sp(h^*). Our algorithm relies on a novel subroutine, Projected Mitigated Extended Value Iteration (PMEVI), to compute bias-constrained optimal policies efficiently. This subroutine can be applied to various previous algorithms to improve regret bounds.

Future- or return-conditioned supervised learning is an emerging paradigm for offline reinforcement learning (RL), where the future outcome (i.e., return) associated with an observed action sequence is used as input to a policy trained to imitate those same actions. While return-conditioning is at the heart of popular algorithms such as decision transformer (DT), these methods tend to perform poorly in highly stochastic environments, where an occasional high return can arise from randomness in the environment rather than the actions themselves. Such situations can lead to a learned policy that is inconsistent with its conditioning inputs; i.e., using the policy to act in the environment, when conditioning on a specific desired return, leads to a distribution of real returns that is wildly different than desired. In this work, we propose the dichotomy of control (DoC), a future-conditioned supervised learning framework that separates mechanisms within a policy's control (actions) from those beyond a policy's control (environment stochasticity). We achieve this separation by conditioning the policy on a latent variable representation of the future, and designing a mutual information constraint that removes any information from the latent variable associated with randomness in the environment. Theoretically, we show that DoC yields policies that are consistent with their conditioning inputs, ensuring that conditioning a learned policy on a desired high-return future outcome will correctly induce high-return behavior. Empirically, we show that DoC is able to achieve significantly better performance than DT on environments that have highly stochastic rewards and transition

We investigate the sets of joint probability distributions that maximize the average multi-information over a collection of margins. These functionals serve as proxies for maximizing the multi-information of a set of variables or the mutual information of two subsets of variables, at a lower computation and estimation complexity. We describe the maximizers and their relations to the maximizers of the multi-information and the mutual information.

We consider strategy proof mechanisms for facility location which maximize equitability between agents. As is common in the literature, we measure equitability with the Gini index. We first prove a simple but fundamental impossibility result that no strategy proof mechanism can bound the approximation ratio of the optimal Gini index of utilities for one or more facilities. We propose instead computing approximation ratios of the complemented Gini index of utilities, and consider how well both deterministic and randomized mechanisms approximate this. In addition, as Nash welfare is often put forwards as an equitable compromise between egalitarian and utilitarian outcomes, we consider how well mechanisms approximate the Nash welfare.

Bayesian optimisation is a popular, surrogate model-based approach for optimising expensive black-box functions. Given a surrogate model, the next location to expensively evaluate is chosen via maximisation of a cheap-to-query acquisition function. We present an epsilon-greedy procedure for Bayesian optimisation in batch settings in which the black-box function can be evaluated multiple times in parallel. Our epsilon-shotgun algorithm leverages the model's prediction, uncertainty, and the approximated rate of change of the landscape to determine the spread of batch solutions to be distributed around a putative location. The initial target location is selected either in an exploitative fashion on the mean prediction, or -- with probability epsilon -- from elsewhere in the design space. This results in locations that are more densely sampled in regions where the function is changing rapidly and in locations predicted to be good (i.e close to predicted optima), with more scattered samples in regions where the function is flatter and/or of poorer quality. We empirically evaluate the epsilon-shotgun methods on a range of synthetic functions and two real-world problems, finding that they perform at least as well as state-of-the-art batch methods and in many cases exceed their performance.

Designing an optimum portfolio that allocates weights to its constituent stocks in a way that achieves the best trade-off between the return and the risk is a challenging research problem. The classical mean-variance theory of portfolio proposed by Markowitz is found to perform sub-optimally on the real-world stock market data since the error in estimation for the expected returns adversely affects the performance of the portfolio. This paper presents three approaches to portfolio design, viz, the minimum risk portfolio, the optimum risk portfolio, and the Eigen portfolio, for seven important sectors of the Indian stock market. The daily historical prices of the stocks are scraped from Yahoo Finance website from January 1, 2016, to December 31, 2020. Three portfolios are built for each of the seven sectors chosen for this study, and the portfolios are analyzed on the training data based on several metrics such as annualized return and risk, weights assigned to the constituent stocks, the correlation heatmaps, and the principal components of the Eigen portfolios. Finally, the optimum risk portfolios and the Eigen portfolios for all sectors are tested on their return over a period of a six-month period. The performances of the portfolios are compared and the portfolio yielding the higher return for each sector is identified.

Algorithmic Recourse (AR) is the problem of computing a sequence of actions that -- once performed by a user -- overturns an undesirable machine decision. It is paramount that the sequence of actions does not require too much effort for users to implement. Yet, most approaches to AR assume that actions cost the same for all users, and thus may recommend unfairly expensive recourse plans to certain users. Prompted by this observation, we introduce PEAR, the first human-in-the-loop approach capable of providing personalized algorithmic recourse tailored to the needs of any end-user. PEAR builds on insights from Bayesian Preference Elicitation to iteratively refine an estimate of the costs of actions by asking choice set queries to the target user. The queries themselves are computed by maximizing the Expected Utility of Selection, a principled measure of information gain accounting for uncertainty on both the cost estimate and the user's responses. PEAR integrates elicitation into a Reinforcement Learning agent coupled with Monte Carlo Tree Search to quickly identify promising recourse plans. Our empirical evaluation on real-world datasets highlights how PEAR produces high-quality personalized recourse in only a handful of iterations.

Off-policy actor-critic methods in reinforcement learning train a critic with temporal-difference updates and use it as a learning signal for the policy (actor). This design typically achieves higher sample efficiency than purely on-policy methods. However, critic networks tend to overestimate value estimates systematically. This is often addressed by introducing a pessimistic bias based on uncertainty estimates. Current methods employ ensembling to quantify the critic's epistemic uncertainty-uncertainty due to limited data and model ambiguity-to scale pessimistic updates. In this work, we propose a new algorithm called Stochastic Actor-Critic (STAC) that incorporates temporal (one-step) aleatoric uncertainty-uncertainty arising from stochastic transitions, rewards, and policy-induced variability in Bellman targets-to scale pessimistic bias in temporal-difference updates, rather than relying on epistemic uncertainty. STAC uses a single distributional critic network to model the temporal return uncertainty, and applies dropout to both the critic and actor networks for regularization. Our results show that pessimism based on a distributional critic alone suffices to mitigate overestimation, and naturally leads to risk-averse behavior in stochastic environments. Introducing dropout further improves training stability and performance by means of regularization. With this design, STAC achieves improved computational efficiency using a single distributional critic network.

The optimal stopping problem is a category of decision problems with a specific constrained configuration. It is relevant to various real-world applications such as finance and management. To solve the optimal stopping problem, state-of-the-art algorithms in dynamic programming, such as the least-squares Monte Carlo (LSMC), are employed. This type of algorithm relies on path simulations using only the last price of the underlying asset as a state representation. Also, the LSMC was thinking for option valuation where risk-neutral probabilities can be employed to account for uncertainty. However, the general optimal stopping problem goals may not fit the requirements of the LSMC showing auto-correlated prices. We employ a data-driven method that uses Monte Carlo simulation to train and test artificial neural networks (ANN) to solve the optimal stopping problem. Using ANN to solve decision problems is not entirely new. We propose a different architecture that uses convolutional neural networks (CNN) to deal with the dimensionality problem that arises when we transform the whole history of prices into a Markovian state. We present experiments that indicate that our proposed architecture improves results over the previous implementations under specific simulated time series function sets. Lastly, we employ our proposed method to compare the optimal exercise of the financial options problem with the LSMC algorithm. Our experiments show that our method can capture more accurate exercise opportunities when compared to the LSMC. We have outstandingly higher (above 974\% improvement) expected payoff from these exercise policies under the many Monte Carlo simulations that used the real-world return database on the out-of-sample (test) data.

We study the problem of learning in the stochastic shortest path (SSP) setting, where an agent seeks to minimize the expected cost accumulated before reaching a goal state. We design a novel model-based algorithm EB-SSP that carefully skews the empirical transitions and perturbs the empirical costs with an exploration bonus to induce an optimistic SSP problem whose associated value iteration scheme is guaranteed to converge. We prove that EB-SSP achieves the minimax regret rate O(B_{star} S A K), where K is the number of episodes, S is the number of states, A is the number of actions, and B_{star} bounds the expected cumulative cost of the optimal policy from any state, thus closing the gap with the lower bound. Interestingly, EB-SSP obtains this result while being parameter-free, i.e., it does not require any prior knowledge of B_{star}, nor of T_{star}, which bounds the expected time-to-goal of the optimal policy from any state. Furthermore, we illustrate various cases (e.g., positive costs, or general costs when an order-accurate estimate of T_{star} is available) where the regret only contains a logarithmic dependence on T_{star}, thus yielding the first (nearly) horizon-free regret bound beyond the finite-horizon MDP setting.

The framework of reinforcement learning or optimal control provides a mathematical formalization of intelligent decision making that is powerful and broadly applicable. While the general form of the reinforcement learning problem enables effective reasoning about uncertainty, the connection between reinforcement learning and inference in probabilistic models is not immediately obvious. However, such a connection has considerable value when it comes to algorithm design: formalizing a problem as probabilistic inference in principle allows us to bring to bear a wide array of approximate inference tools, extend the model in flexible and powerful ways, and reason about compositionality and partial observability. In this article, we will discuss how a generalization of the reinforcement learning or optimal control problem, which is sometimes termed maximum entropy reinforcement learning, is equivalent to exact probabilistic inference in the case of deterministic dynamics, and variational inference in the case of stochastic dynamics. We will present a detailed derivation of this framework, overview prior work that has drawn on this and related ideas to propose new reinforcement learning and control algorithms, and describe perspectives on future research.

We consider a combinatorial multi-armed bandit problem for maximum value reward function under maximum value and index feedback. This is a new feedback structure that lies in between commonly studied semi-bandit and full-bandit feedback structures. We propose an algorithm and provide a regret bound for problem instances with stochastic arm outcomes according to arbitrary distributions with finite supports. The regret analysis rests on considering an extended set of arms, associated with values and probabilities of arm outcomes, and applying a smoothness condition. Our algorithm achieves a O((k/Delta)log(T)) distribution-dependent and a O(T) distribution-independent regret where k is the number of arms selected in each round, Delta is a distribution-dependent reward gap and T is the horizon time. Perhaps surprisingly, the regret bound is comparable to previously-known bound under more informative semi-bandit feedback. We demonstrate the effectiveness of our algorithm through experimental results.

We develop an econometric framework integrating heavy-tailed Student's t distributions with behavioral probability weighting while preserving infinite divisibility. Using 432{,}752 observations across 86 assets (2004--2024), we demonstrate Student's t specifications outperform Gaussian models in 88.4\% of cases. Bounded probability-weighting transformations preserve mathematical properties required for dynamic pricing. Gaussian models underestimate 99\% Value-at-Risk by 19.7\% versus 3.2\% for our specification. Joint estimation procedures identify tail and behavioral parameters with established asymptotic properties. Results provide robust inference for asset-pricing applications where heavy tails and behavioral distortions coexist.

The observed similarities in the behavior of humans and Large Language Models (LLMs) have prompted researchers to consider the potential of using LLMs as models of human cognition. However, several significant challenges must be addressed before LLMs can be legitimately regarded as cognitive models. For instance, LLMs are trained on far more data than humans typically encounter, and may have been directly trained on human data in specific cognitive tasks or aligned with human preferences. Consequently, the origins of these behavioral similarities are not well understood. In this paper, we propose a novel way to enhance the utility of LLMs as cognitive models. This approach involves (i) leveraging computationally equivalent tasks that both an LLM and a rational agent need to master for solving a cognitive problem and (ii) examining the specific task distributions required for an LLM to exhibit human-like behaviors. We apply this approach to decision-making -- specifically risky and intertemporal choice -- where the key computationally equivalent task is the arithmetic of expected value calculations. We show that an LLM pretrained on an ecologically valid arithmetic dataset, which we call Arithmetic-GPT, predicts human behavior better than many traditional cognitive models. Pretraining LLMs on ecologically valid arithmetic datasets is sufficient to produce a strong correspondence between these models and human decision-making. Our results also suggest that LLMs used as cognitive models should be carefully investigated via ablation studies of the pretraining data.

Online advertising has recently grown into a highly competitive and complex multi-billion-dollar industry, with advertisers bidding for ad slots at large scales and high frequencies. This has resulted in a growing need for efficient "auto-bidding" algorithms that determine the bids for incoming queries to maximize advertisers' targets subject to their specified constraints. This work explores efficient online algorithms for a single value-maximizing advertiser under an increasingly popular constraint: Return-on-Spend (RoS). We quantify efficiency in terms of regret relative to the optimal algorithm, which knows all queries a priori. We contribute a simple online algorithm that achieves near-optimal regret in expectation while always respecting the specified RoS constraint when the input sequence of queries are i.i.d. samples from some distribution. We also integrate our results with the previous work of Balseiro, Lu, and Mirrokni [BLM20] to achieve near-optimal regret while respecting both RoS and fixed budget constraints. Our algorithm follows the primal-dual framework and uses online mirror descent (OMD) for the dual updates. However, we need to use a non-canonical setup of OMD, and therefore the classic low-regret guarantee of OMD, which is for the adversarial setting in online learning, no longer holds. Nonetheless, in our case and more generally where low-regret dynamics are applied in algorithm design, the gradients encountered by OMD can be far from adversarial but influenced by our algorithmic choices. We exploit this key insight to show our OMD setup achieves low regret in the realm of our algorithm.

We study principal-agent problems in which a principal commits to an outcome-dependent payment scheme -- called contract -- in order to induce an agent to take a costly, unobservable action leading to favorable outcomes. We consider a generalization of the classical (single-round) version of the problem in which the principal interacts with the agent by committing to contracts over multiple rounds. The principal has no information about the agent, and they have to learn an optimal contract by only observing the outcome realized at each round. We focus on settings in which the size of the agent's action space is small. We design an algorithm that learns an approximately-optimal contract with high probability in a number of rounds polynomial in the size of the outcome space, when the number of actions is constant. Our algorithm solves an open problem by Zhu et al.[2022]. Moreover, it can also be employed to provide a mathcal{O}(T^{4/5}) regret bound in the related online learning setting in which the principal aims at maximizing their cumulative utility, thus considerably improving previously-known regret bounds.

We study regret minimization for reinforcement learning (RL) in Latent Markov Decision Processes (LMDPs) with context in hindsight. We design a novel model-based algorithmic framework which can be instantiated with both a model-optimistic and a value-optimistic solver. We prove an O(mathsf{Var^star M Gamma S A K}) regret bound where O hides logarithm factors, M is the number of contexts, S is the number of states, A is the number of actions, K is the number of episodes, Gamma le S is the maximum transition degree of any state-action pair, and Var^star is a variance quantity describing the determinism of the LMDP. The regret bound only scales logarithmically with the planning horizon, thus yielding the first (nearly) horizon-free regret bound for LMDP. This is also the first problem-dependent regret bound for LMDP. Key in our proof is an analysis of the total variance of alpha vectors (a generalization of value functions), which is handled with a truncation method. We complement our positive result with a novel Omega(mathsf{Var^star M S A K}) regret lower bound with Gamma = 2, which shows our upper bound minimax optimal when Gamma is a constant for the class of variance-bounded LMDPs. Our lower bound relies on new constructions of hard instances and an argument inspired by the symmetrization technique from theoretical computer science, both of which are technically different from existing lower bound proof for MDPs, and thus can be of independent interest.

Simulated annealing (SA) is a stochastic global optimisation technique applicable to a wide range of discrete and continuous variable problems. Despite its simplicity, the development of an effective SA optimiser for a given problem hinges on a handful of carefully handpicked components; namely, neighbour proposal distribution and temperature annealing schedule. In this work, we view SA from a reinforcement learning perspective and frame the proposal distribution as a policy, which can be optimised for higher solution quality given a fixed computational budget. We demonstrate that this Neural SA with such a learnt proposal distribution, parametrised by small equivariant neural networks, outperforms SA baselines on a number of problems: Rosenbrock's function, the Knapsack problem, the Bin Packing problem, and the Travelling Salesperson problem. We also show that Neural SA scales well to large problems - generalising to significantly larger problems than the ones seen during training - while achieving comparable performance to popular off-the-shelf solvers and other machine learning methods in terms of solution quality and wall-clock time.

Entropy regularization is a standard technique in reinforcement learning (RL) to enhance exploration, yet it yields negligible effects or even degrades performance in Large Language Models (LLMs). We attribute this failure to the cumulative tail risk inherent to LLMs with massive vocabularies and long generation horizons. In such environments, standard global entropy maximization indiscriminately dilutes probability mass into the vast tail of invalid tokens rather than focusing on plausible candidates, thereby disrupting coherent reasoning. To address this, we propose Trust Region Entropy (TRE), a method that encourages exploration strictly within the model's trust region. Extensive experiments across mathematical reasoning (MATH), combinatorial search (Countdown), and preference alignment (HH) tasks demonstrate that TRE consistently outperforms vanilla PPO, standard entropy regularization, and other exploration baselines. Our code is available at https://github.com/WhyChaos/TRE-Encouraging-Exploration-in-the-Trust-Region.

We address the problem of planning in an environment with deterministic dynamics and stochastic rewards with discounted returns. The optimal value function is not known, nor are the rewards bounded. We propose Platypoos, a simple scale-free planning algorithm that adapts to the unknown scale and smoothness of the reward function. We provide a sample complexity analysis for Platypoos that improves upon prior work and holds simultaneously over a broad range of discount factors and reward scales, without the algorithm knowing them. We also establish a matching lower bound showing our analysis is optimal up to constants.

We improve the efficiency of algorithms for stochastic combinatorial semi-bandits. In most interesting problems, state-of-the-art algorithms take advantage of structural properties of rewards, such as independence. However, while being optimal in terms of asymptotic regret, these algorithms are inefficient. In our paper, we first reduce their implementation to a specific submodular maximization. Then, in case of matroid constraints, we design adapted approximation routines, thereby providing the first efficient algorithms that rely on reward structure to improve regret bound. In particular, we improve the state-of-the-art efficient gap-free regret bound by a factor m/log m, where m is the maximum action size. Finally, we show how our improvement translates to more general budgeted combinatorial semi-bandits.

Accurate prediction of future prices of stocks is a difficult task to perform. Even more challenging is to design an optimized portfolio with weights allocated to the stocks in a way that optimizes its return and the risk. This paper presents a systematic approach towards building two types of portfolios, optimum risk, and eigen, for four critical economic sectors of India. The prices of the stocks are extracted from the web from Jan 1, 2016, to Dec 31, 2020. Sector-wise portfolios are built based on their ten most significant stocks. An LSTM model is also designed for predicting future stock prices. Six months after the construction of the portfolios, i.e., on Jul 1, 2021, the actual returns and the LSTM-predicted returns for the portfolios are computed. A comparison of the predicted and the actual returns indicate a high accuracy level of the LSTM model.

We consider finite-horizon Markov Decision Processes where parameters, such as transition probabilities, are unknown and estimated from data. The popular distributionally robust approach to addressing the parameter uncertainty can sometimes be overly conservative. In this paper, we propose a new formulation, Bayesian risk Markov Decision Process (BR-MDP), to address parameter uncertainty in MDPs, where a risk functional is applied in nested form to the expected total cost with respect to the Bayesian posterior distribution of the unknown parameters. The proposed formulation provides more flexible risk attitutes towards parameter uncertainty and takes into account the availability of data in future times stages. To solve the proposed formulation with the conditional value-at-risk (CVaR) risk functional, we propose an efficient approximation algorithm by deriving an analytical approximation of the value function and utilizing the convexity of CVaR. We demonstrate the empirical performance of the BR-MDP formulation and proposed algorithms on a gambler's betting problem and an inventory control problem.

It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various machine learning methods have recently been developed with the goal to let the learner also represent its epistemic uncertainty, i.e., the uncertainty caused by a lack of knowledge and data. An emerging branch of the literature proposes the use of a second-order learner that provides predictions in terms of distributions on probability distributions. However, recent work has revealed serious theoretical shortcomings for second-order predictors based on loss minimisation. In this paper, we generalise these findings and prove a more fundamental result: There seems to be no loss function that provides an incentive for a second-order learner to faithfully represent its epistemic uncertainty in the same manner as proper scoring rules do for standard (first-order) learners. As a main mathematical tool to prove this result, we introduce the generalised notion of second-order scoring rules.

Cascading bandits have gained popularity in recent years due to their applicability to recommendation systems and online advertising. In the cascading bandit model, at each timestep, an agent recommends an ordered subset of items (called an item list) from a pool of items, each associated with an unknown attraction probability. Then, the user examines the list, and clicks the first attractive item (if any), and after that, the agent receives a reward. The goal of the agent is to maximize the expected cumulative reward. However, the prior literature on cascading bandits ignores the influences of user states (e.g., historical behaviors) on recommendations and the change of states as the session proceeds. Motivated by this fact, we propose a generalized cascading RL framework, which considers the impact of user states and state transition into decisions. In cascading RL, we need to select items not only with large attraction probabilities but also leading to good successor states. This imposes a huge computational challenge due to the combinatorial action space. To tackle this challenge, we delve into the properties of value functions, and design an oracle BestPerm to efficiently find the optimal item list. Equipped with BestPerm, we develop two algorithms CascadingVI and CascadingBPI, which are both computationally-efficient and sample-efficient, and provide near-optimal regret and sample complexity guarantees. Furthermore, we present experiments to show the improved computational and sample efficiencies of our algorithms compared to straightforward adaptations of existing RL algorithms in practice.

Provably efficient Model-Based Reinforcement Learning (MBRL) based on optimism or posterior sampling (PSRL) is ensured to attain the global optimality asymptotically by introducing the complexity measure of the model. However, the complexity might grow exponentially for the simplest nonlinear models, where global convergence is impossible within finite iterations. When the model suffers a large generalization error, which is quantitatively measured by the model complexity, the uncertainty can be large. The sampled model that current policy is greedily optimized upon will thus be unsettled, resulting in aggressive policy updates and over-exploration. In this work, we propose Conservative Dual Policy Optimization (CDPO) that involves a Referential Update and a Conservative Update. The policy is first optimized under a reference model, which imitates the mechanism of PSRL while offering more stability. A conservative range of randomness is guaranteed by maximizing the expectation of model value. Without harmful sampling procedures, CDPO can still achieve the same regret as PSRL. More importantly, CDPO enjoys monotonic policy improvement and global optimality simultaneously. Empirical results also validate the exploration efficiency of CDPO.

Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty. Predictive uncertainty is commonly measured by the entropy of the Bayesian model average (BMA) predictive distribution. Yet, the properness of this current measure of predictive uncertainty was recently questioned. We provide new insights regarding those limitations. Our analyses show that the current measure erroneously assumes that the BMA predictive distribution is equivalent to the predictive distribution of the true model that generated the dataset. Consequently, we introduce a theoretically grounded measure to overcome these limitations. We experimentally verify the benefits of our introduced measure of predictive uncertainty. We find that our introduced measure behaves more reasonably in controlled synthetic tasks. Moreover, our evaluations on ImageNet demonstrate that our introduced measure is advantageous in real-world applications utilizing predictive uncertainty.

In this work we study agents in simulated bargaining scenarios, where a buyer and a seller communicate through a text channel and attempt to negotiate mutually beneficial trades, under different information regimes (complete information, information asymmetry or mutual uncertainty). We evaluate their performance w.r.t. game-theoretical solutions and further investigate their honesty (their tendency to disclose or withhold information or to mislead and deceive) as well as their credulity (their tendency to trust or distrust information provided by the other agent). We study zero-shot LLM agents with simple prompting scaffolding as well as fine-tuned agents, in order to investigate whether optimising the agents to maximise financial profits makes them stronger negotiators but also more dishonest and less trusting. We find that off-the-shelf LLMs all substantially deviate from game-theoretical equilibria, they attempt to lie about their private information but cannot efficiently exploit information asymmetries. Fine-tuning on financial utility makes the agents stronger at achieving better deals but also more dishonest, highlighting the risks that optimising agents for a task can have on their safety. We release our code and a dataset of bargaining scenarios.

Stochastic optimization is one of the central problems in Machine Learning and Theoretical Computer Science. In the standard model, the algorithm is given a fixed distribution known in advance. In practice though, one may acquire at a cost extra information to make better decisions. In this paper, we study how to buy information for stochastic optimization and formulate this question as an online learning problem. Assuming the learner has an oracle for the original optimization problem, we design a 2-competitive deterministic algorithm and a e/(e-1)-competitive randomized algorithm for buying information. We show that this ratio is tight as the problem is equivalent to a robust generalization of the ski-rental problem, which we call super-martingale stopping. We also consider an adaptive setting where the learner can choose to buy information after taking some actions for the underlying optimization problem. We focus on the classic optimization problem, Min-Sum Set Cover, where the goal is to quickly find an action that covers a given request drawn from a known distribution. We provide an 8-competitive algorithm running in polynomial time that chooses actions and decides when to buy information about the underlying request.