Marielle Brunette
email: marielle.brunette@inra.fr

Jonas Ngouhouo-Poufoun

Documents de travail

Keywords: field experiment, risk aversion, ordered lottery selection, preferences, farmers. JEL codes: C93, D81

We compare individual risk preferences elicited through a classic Ordered Lottery Selection (OLS) procedure with five gambles, and an extended procedure composed of nine gambles. The research question is about the stability of the risk preferences across these two elicitation variants. We implemented a field experiment with 1002 rural households in the Congo Basin from December 2013 to July 2014. We show that 1/3 of the sample is extremely risk averse regardless of the procedure. We found inconsistencies in risk preferences elicited across procedures. Indeed, 45.71% are characterized by instability of preferences, either weak (34.53%) or strong (11.18%); 42.81% of the sample exhibits stable preferences and the remaining 11.48% of the sample -initially risk neutral in the classic procedure -is classified as risk loving in the extended procedure. Undereducation can be seen as the main driver of the strong instability since the incremental change brought about by the attainment of secondary school on the likelihood to remain stable is ten times greater than the other considered drivers.

Introduction

Risk preferences are known to be an important determinant of most of the decisions regarding risk.

As a consequence, experimental economics has developed procedures to quantify these risk preferences. The two most common procedures are the Multiple Price List (MPL) method, popularized by [START_REF] Holt | Risk aversion and incentive effects[END_REF], and the Ordered Lottery Selection (OLS) method, proposed by [START_REF] Binswanger | Attitudes toward risk: Experimental measurement in rural India[END_REF] and popularized by [START_REF] Eckel | Forecasting risk attitudes: An experimental study using actual and forecast gamble choices[END_REF]. Other methods also appear in the literature such as the certainty equivalent approach, the Becker-DeGroot-Marschak auction or the method proposed by [START_REF] Gneezy | An experiment on risk taking and evaluation periods[END_REF].

These methods are largely used in economics to measure risk preferences, and some studies compare the results obtained with different methods. For example, [START_REF] Dave | Eliciting risk preferences: When is simple better?[END_REF] showed that risk aversion is, on average, higher with a MPL procedure than with an OLS procedure. [START_REF] Reynaud | Stability of risk preference measures: Results from a field experiment on French farmers[END_REF] found the opposite result. [START_REF] Anderson | Are risk preferences stable? Comparing an experimental measure with a validated survey-based measure[END_REF] compared risk preferences measurement between an experiment and a survey. They found that only the individual's risk preferences classification from inheritance-based gambles are in-line with experimental measurements.

Other comparisons appeared for elicitation techniques [START_REF] Berg | Risk preference instability across institutions: A dilemna[END_REF], [START_REF] Deck | Measuring risk attitudes controlling for personality traits[END_REF], [START_REF] Chuang | Stability of experimental and survey measures of risk, time, and social preferences: A review and some new results[END_REF]) but with an unanimous conclusion: elicited risk preferences are proceduredependent, and risk preferences tend to be more stable when the elicitation procedures are similar to one another [START_REF] Choi | Consistency and heterogeneity of individual behavior under uncertainty[END_REF], [START_REF] Chuang | Stability of experimental and survey measures of risk, time, and social preferences: A review and some new results[END_REF]).

In this paper, rather than comparing two different elicitation techniques, we focus on two variants of the same procedure. Contrary to the other existing procedures, classic OLS procedure as proposed by [START_REF] Eckel | Forecasting risk attitudes: An experimental study using actual and forecast gamble choices[END_REF] does not allow the precise identification of risk loving preferences. Indeed, risk neutrality and risk loving are expressed in the same last gamble choice, and are then impossible to disentangle. In this context, several interesting questions emerge: How much individuals selecting this last gamble are risk loving and at which degree ? Are individual's preferences towards risk stable across elicitation procedures ? If not, are there different degrees of instability ? What are the driving factors of the instability ?

To address these questions, we conducted a field experiment in which we elicited risk preferences through a classic OLS procedure composed of five gambles and an extended OLS procedure composed of nine gambles, and allowed the elicitation of different degrees of risk loving compared to the classic OLS. This experiment contributes to the debate on the stability of individual prefer-ences across elicitation procedures. The experiment is implemented on 1002 rural households in the Congo Basin. Rural households in developing countries are a common sample for elicitation of risk preferences via the OLS procedure [START_REF] Binswanger | Attitudes toward risk: Experimental measurement in rural India[END_REF], [START_REF] Chuang | Stability of experimental and survey measures of risk, time, and social preferences: A review and some new results[END_REF]).

We categorized the sample function of the (in)stability of the head of households' risk preferences between the two OLS variants. Specifically, we showed that 42.81% of the sample belongs to the category "stable preferences", 34.53% have a "weak instability", while 11.18% have a "strong instability". The remaining of the sample were households who are fundamentally risk loving and were constrained by the classic elicitation procedure (11.48%). We then considered household assets and socioeconomic characteristics to estimate a statistical model to characterize instability and derive its potential drivers.

The paper is organized as follows. We first describe the experimental design and the two elicitation variants. Second, we present the results focusing on the preferences of the households towards risk and the stability (or not) of these preferences. Third, we analyze the potential drivers of the instability. Finally, we provide a discussion and a conclusion.

Experimental design and procedures

The experiment was realized in the field on a sample of 1002 rural households in the Congo basin from December 2013 to July 2014. The experiment took place in the Dja-Odzala-Minkébé transboundary conservation landscape (Tridom), which spans Cameroon, Gabon and Congo.

The OLS experiment was realized during a face-to-face survey as part of a larger questionnaire aiming at assessing "rural households livelihoods system, deforestation and biodiversity conservation".

A short summary of the questionnaire is provided in Appendix A, while the interested reader is referred to [START_REF] Ngouhouo Poufoun | The value of endangered forest elephants to local communities in a transboundary conservation landscape[END_REF] for a complete overview.

The experiment was purely hypothetical, in the sense that no financial incentives were provided to the subjects. This choice was driven by several reasons. First, [START_REF] Camerer | The effects of financial incentives in experiments: A review and capital-labor-production framework[END_REF] and [START_REF] Beattie | The impact of incentives upon risky choice experiments[END_REF] showed that, since questions are related to simple lottery choices, monetary incentives do not significantly affect decision-making. In the same vein, some papers show no difference between decisions made with hypothetical or real payoffs [START_REF] Battalio | Testing between alternative models of choice under uncertainty: Some initial results[END_REF][START_REF] Wik | On the measurement of risk aversion from experimental data[END_REF]). Finally, [START_REF] Chuang | Stability of experimental and survey measures of risk, time, and social preferences: A review and some new results[END_REF] found no difference in the stability of hypothetical versus incentivized measure of risk preferences. However, to facilitate the understanding, matchboxes were used to represent the lottery choices (probabilities and payoffs), and households kept the box at the end of the experiment.

We elicited individual's risk preferences through two OLS procedures. We used a within-subjects design so that each of the 1002 household's head performed both procedures. The first one, presented in Table 1, is a classic OLS procedure as proposed by [START_REF] Eckel | Forecasting risk attitudes: An experimental study using actual and forecast gamble choices[END_REF] in which an individual must choose among five gambles the one s/he accepts to play for. Each gamble consists of two payoffs, each of which is obtained at the same probability of 50%. The choice of a gamble allows one to infer an interval for the relative risk aversion coefficient, supposing that subjects have a constant relative risk aversion utility function of the form U = x (1-r) /(1 -r), where r is the relative risk aversion coefficient. This specification implies risk neutrality for r = 0 and risk aversion for r > 0.

In this procedure, gambles 1 to 4 correspond to different degrees of risk aversion. The individual who choose Gamble 5 may be risk neutral or risk loving. The procedure does not allow one to disentangle the latter two categories of preferences towards risk. Note that in the classic OLS procedure, the initial payoffs proposed in [START_REF] Eckel | Forecasting risk attitudes: An experimental study using actual and forecast gamble choices[END_REF] are divided by four, while in the extended OLS procedure, the initial payoffs are multiplied by 2.5 [START_REF] Reynaud | Stability of risk preference measures: Results from a field experiment on French farmers[END_REF]. As a result, the implied ranges for the coefficient of relative risk aversion are not modified.

Consequently, by comparing preferences elicited in classic procedure and the ones elicited through the extended one, we capture both the effect of the level of the payoffs and the effect of increasing the number of possible gambles. Concerning the effect of the payoff, [START_REF] Holt | Risk aversion and incentive effects[END_REF] and [START_REF] Reynaud | Stability of risk preference measures: Results from a field experiment on French farmers[END_REF] found that individual's preferences are largely unaffected when hypothetical payoffs are scaled up. Concerning the effect of the increasing number of possible gambles, we expect that the average risk aversion reduces. Indeed, in the extended procedure some gamble choices correspond to negative risk aversion coefficients, so that, on average, the risk aversion of the whole sample should decrease. However, the question remains if those who are risk loving with the extended procedure are only among those who selected Gamble 5 in the classic OLS procedure or if some risk averse individuals reversed their preferences.

3 Risk preferences and the stability: Analysis and results

In this section, we present the results of our elicitation of household risk preferences and, based on these results, we propose a categorization of households with regard to the stability (or not) of their preferences towards risk.

Individual's risk preferences elicitation

Table 3 presents the results of the experiment where columns are the five gambles of the classic procedure, and rows the nine gambles of the extended procedure.

Table 3 shows that in the classic procedure, 163 individuals are classified as risk neutral/risk loving (choice of Gamble 5) while the 839 others are risk averse (choice of gamble 1 to 4). In the extended Table 3 allows the observation of high selections of extreme preferences towards risk. For both procedures, the highest frequency is for extreme risk aversion, i.e. the choice of Gamble 1. Indeed, more than 30% of the sample was revealed to be extremely risk averse. In this sense, the two procedures are consistent one with another, at least for extremely risk-averse individuals. This result comes from the fact that the first gamble is not risky, in the sense that the payoff is certain.

Individuals may be sensitive to this certainty, which explains the high proportion of the sample that chose Gamble 1 in the two procedures. This idea is confirmed by follow-up questions at the end of the experiment where subjects may justify their choices. Those selecting Gamble 1 said "I don't like to play", "I don't want to take risk", "I'm prudent", etc. A high frequency is also observe for extreme risk loving in the extended procedure, i.e. the choice of Gamble 9. Of the 227 individuals who chose gamble 7 to 9, 58.15% selected Gamble 9, and are therefore very risk loving. This result is similar to that of [START_REF] Reynaud | Stability of risk preference measures: Results from a field experiment on French farmers[END_REF], in the sense that 21% of their sample was characterized as risk loving, with a more pronounced concentration in the extreme. Indeed, in their experiment risk lovers only selected Gamble 9.

Using the center of the ranges for the relative risk aversion coefficient (Table 1 andTable 2), we can compute an average risk aversion coefficient1 . This average coefficient is 1.025 for the classic OLS procedure and 0.608 for the extended OLS procedure. A Student's t-test for mean comparison reveals that the average coefficients are statistically different from each other at the 0.01% level. [START_REF] Arrow | Essays in the theory of risk-bearing[END_REF] suggested that individuals' coefficients of relative risk aversion should be approximately 1. [START_REF] Kydland | Time to build and aggregate fluctuations[END_REF] found coefficients of relative risk aversion in the range of 0 to 2. However, the coefficient elicited through the extended procedure is closer to the estimates obtained in previous studies: 0. Moreover, the Spearman correlation coefficient allows for the comparison of the individuals' choice across procedures. We observed a positive and significant correlation (ρ = 0.69) of risk preferences between both the procedures. This result is in accordance with the main finding in the literature.

Indeed, [START_REF] Deck | Measuring risk aversion on multiple tasks: Can domain specific risk attitudes explain apparently inconsistent behavior ? Working paper[END_REF] and [START_REF] Reynaud | Stability of risk preference measures: Results from a field experiment on French farmers[END_REF] found a positive and significant correlation between the risk preferences elicited through Holt and Laury's task and Eckel and Grossman's task (ρ = 0.21 and ρ = 0.4, respectively). Our correlation is stronger, probably because we compare two variants of the same procedure.

To conclude, we have two possible effects at work: a payoff effect (expected to have no effect on risk preferences) and an effect linked to the increasing number of possible gambles (expected to be negative for risk aversion). Our results revealed that in the extended OLS procedure, as compared to the classic one, a lower proportion of the sample is risk averse and the average risk aversion coefficient is lower, suggesting that the payoff effect is non-existent in this experiment.

Stability (or not) of the preferences towards risk: A categorization

Table 3 allows us to categorize households in regard to the stability of their preferences towards risk. These four categories are represented through different shades of gray in Table 3.

The first category of households includes individuals with "stable preferences" towards risk (white cells in Table 3). [START_REF] Reynaud | Stability of risk preference measures: Results from a field experiment on French farmers[END_REF] consider that preferences are stable across tasks if CRRA ranges are the same between procedures. In our case, the CRRA ranges are not identical and sometimes they overlap. As a consequence, we first consider the choice of the individual in the classic procedure to have her/his CRRA range, and then, we compare this to the gamble choice in the extended procedure, in terms of the risk aversion coefficient. For example, if an individual choses Gamble 1 in the classic procedure, this means that her/his relative risk aversion coefficient is higher than 2 and it is compatible only with the choice of Gamble 1 in the extended procedure.

As a consequence, we assume that an individual who chooses Gamble 1 in the classic procedure has stable preferences only if s/he chooses Gamble 1 in the extended procedure. Another example of stable preferences is an individual choosing Gamble 2 in the classic procedure (0.67 < r < 2)

and gambles 1 or 2 in the extended one. The "stable preferences" category makes up 42.81% of the sample (429 households).

The second category of households is made up of individuals with a "strong instability" of preferences towards risk (light gray cells in Table 3). This category includes 49.43% of risk loving in the extended procedure who expressed risk aversion in the classic procedure. In other words, this category represents individuals who switched from risk aversion in the classic procedure to risk loving in the extended one, i.e. who have reversed their preferences. This category represents 112 households, or 11.18% of the overall sample.

The third category is associated with households who have a "weak instability" of preferences towards risk (medium gray cells in Table 3). It comprises individuals who deviated in the extended procedure from their CRRA range estimated in the classic procedure. For example, if an individual chooses the Gamble 2 in the extended procedure (0.67 < r < 2), s/he is characterized by weak instability if s/he chooses gambles 3, 4, 5 or 6 in the extended procedure. The preferences of 346 households are characterized by "weak instability" (i.e. 34.53%).

The remaining 115 individuals represent the fourth category that we qualify as "false neutral" (dark gray cells in Table 3) in the sense that they choose Gamble 5 in the classic procedure but stated to be risk loving in the extended one. It seems that most of the individuals choosing Gamble 5 in the classic OLS procedure were fundamentally risk loving. The choice of Gamble 5 in the classic procedure reveals that the other options do not fit them, and as a consequence that they are not risk averse. In follow-up questions, we asked subjects to explain their choice. Individuals choosing Gamble 5 in the classic procedure and gambles 7, 8 or 9 in the extended ones indicated the following reasons among others: "I like to take risk" or "I'm attracted by potential big gains".

Final important result is that the lower the risk aversion in the classic procedure, the higher the chance to be risk loving in the extended procedure. Indeed, we observe that among individuals who choose Gamble 1 in the classic procedure, 10 reversed their preferences, switching from risk aversion to risk loving, in the extended procedure. The number of individuals who reversed their preferences is 24 when choosing Gamble 2 in the classic procedure, 32 when choosing Gamble 3, and 46 when choosing Gamble 4.

Drivers of risk preferences instability

The experiment represents a part of a larger survey. In this section, we used variables coming from a questionnaire submitted to the households during the larger survey to try to explain (in)stability.

Section 4.1 describes the descriptive statistics associated with these variables whereas Section 4.2 presents the econometric results of a probit analysis designed to identify the potential drivers of instability.

Some descriptive statistics of the sample

Table 4 reports the descriptive statistics of the sample. In the Tridom landscape, the humanelephant-conflict (HEC) is at the heart of the discussion. This specificity is taken into account through three variables: whether heads of households faced such conflicts or not, the elephant density in the neighbourhood and the damage from HEC to crops. We can observe that HEC damages livelihoods of about 27% of households in the study area, generates damages to crop for 90.12 CFA 1000/years on average, and that, on average, 0.93 elephants/hectare are present in the household neighbourhoods. Our intuition is that households confronted to HEC are familiar with the notion of risk and risk management, in which case these three variables likely impact the stability of their risk preferences. In the same vein, the literature shows that exogenous shocks such as natural disasters or violent conflict affect risk preferences (Schildberg-Horisch ( 2018)).

We consider three types of assets: land holding in hectares as an indicator of natural assets, money transfer and access to credit as indicators of financial assets, and membership of a community group of interest2 as an indicator of social assets. We expect households with higher assets being more stable.

We expect educated households to be prone to stability. We then ask whether the respondent reached secondary school (the answer is "yes" for 56% of the sample). Indeed, following [START_REF] Choi | Consistency and heterogeneity of individual behavior under uncertainty[END_REF], less educated respondents play less consistently in risk preferences game.

We consider the number of years settled in villages (seniority) with the idea that households who settled long ago may be more prone to stability. The statistics reveal that households resided in a village for an average of 27 years. We include the variable "Baka employment" that is a very low cost-labor force that households may use. In the sample, on average, 1.85 Baka autochtonous per household are employed temporary to realize works in the fields.

Finally, we ask respondents to indicate if they rely on forest products, which is the case for 71% of the sample.

Among socioeconomic features as possible characteristics of instability, we consider marital status (72% of the sample are married), age (an average of 48.40 years), household size (average of 6.45 individuals per household) and gender (sample composed of 76% of male). In particular, we test for gender-specific differences in the stability of risk preferences as proposed by [START_REF] Filippin | A reconsideration of gender differences in risk attitudes[END_REF].

Factors of risk preferences instability across elicitation procedures

The fundamental difference between both variants of OLS procedure considered in this paper resides in the risk loving categories of the extended procedure, giving the opportunity to those classified in the neutral category of the classic OLS procedure to express their risk loving preferences. According to Section 3 above, 115 of the 227 risk lovers identified in the extended procedure hail from the neutral category in the classic OLS procedure and are characterized as "false neutral". The remaining 112 risk lovers hail from the risk averse category in the classic OLS procedure. They reversed their risk preferences and are characterized with "strong instability". In this subsection, we conduct a binary probit analysis to compare the variables associated to households characterized with "strong instability" to those who are "false neutral". As a consequence, comparing these two sub-samples allows identifying potential drivers of the strong instability. Results of the probit regression are presented in Table 5. Conversely, belonging to a community group of interest, experiencing greater damages from HEC, and residence time in the village tend to favor instability. An increase of 1000 CFA of crop damage by elephants implies 0.12 more percentage points to the probability to express unstable risk preferences.

An additional year spent in the village after settlement implies 0.16 more percentage points to the likelihood to express instability. Finally, respondents who are members of a community group of interest are 6.58% more likely to express unstable risk preferences, a finding which is opposite to our expectations.

To conclude, it appears that the marginal effect of education on the likelihood to remain stable is 11.35 percentage points, an amount about ten times greater than other statistically significant drivers. Education improves the understanding of the experimental game and allows a better appraisal of the different gambles, implying more stability in risk preferences. Our result is in accordance with the one of [START_REF] Choi | Consistency and heterogeneity of individual behavior under uncertainty[END_REF].

Discussion

The literature has previously identified potential factors explaining instability of risk preferences [START_REF] Reynaud | Stability of risk preference measures: Results from a field experiment on French farmers[END_REF]).

The first potential driver of instability is the context-dependency of the risk preferences [START_REF] Deck | Measuring risk attitudes controlling for personality traits[END_REF], [START_REF] Barseghyan | Are risk preferences stable across contexts ? Evidence from insurance data[END_REF]). For example, [START_REF] Barseghyan | Are risk preferences stable across contexts ? Evidence from insurance data[END_REF] found that survey participants are characterized by higher risk aversion when the choice is about home insurance as compared to car insurance. However, this potential explanation is not relevant in our experiment because the two elicitation variants are realized exactly in the same framework.

Second, [START_REF] Anderson | Are risk preferences stable? Comparing an experimental measure with a validated survey-based measure[END_REF] and [START_REF] Dave | Eliciting risk preferences: When is simple better?[END_REF] stipulated that differences in cognitive ability of subjects, and task complexity may be relevant drivers. Our result is in line with the first part of this assertion, in the sense that education has a positive and significant impact on stability. This result is in accordance with [START_REF] Dave | Eliciting risk preferences: When is simple better?[END_REF], who observed that Holt and Laury's task leads to more inconsistent choices than Eckel and Grossman's task among individuals with lower mathematical skills. Concerning task complexity, the extended procedure may be considered as more complex since the choice of a gamble is more complicated with nine as opposed to five gambles. However, as [START_REF] Reynaud | Stability of risk preference measures: Results from a field experiment on French farmers[END_REF], we obtain a lower risk aversion with the most complex task.

Third, [START_REF] Choi | Consistency and heterogeneity of individual behavior under uncertainty[END_REF] and [START_REF] Chuang | Stability of experimental and survey measures of risk, time, and social preferences: A review and some new results[END_REF] observed that instability increases when the elicitation procedures are too different. In our experiment, the two procedures are two OLS variants. We can thus think that this driver is not relevant in our case. Moreover, this similarity between the two elicitation procedures may explain why we have a quite high level of stability in our sample (42.81%) and a high correlation coefficient between the individuals' choices in the two procedures (ρ = 0.69).

A last potential driver, puts forward by [START_REF] Bocquého | Expected utility or prospect theory maximisers? Assessing farmers' risk behaviour from field-experiment data[END_REF], is the misspecification of individual preferences. The two procedures that we tested assume an expected utility framework. However, household's head may behave accordingly to other types of preferences, in particular prospect theory (see [START_REF] Reynaud | Stability of risk preference measures: Results from a field experiment on French farmers[END_REF], [START_REF] Bocquého | Expected utility or prospect theory maximisers? Assessing farmers' risk behaviour from field-experiment data[END_REF] and [START_REF] Bougherara | Structural estimation of farmers' risk and ambiguity preferences: A field experiment[END_REF] for French farmers and [START_REF] Harrison | Choice under uncertainty: Evidence from Ethiopia, India and Uganda[END_REF] for African farmers); such an explanation may be relevant in our case and may be interesting question for future research.

Conclusion

This paper deals with a fundamental question in experimental economics of preferences towards risk: Are risk preferences stable ? Our paper contributes to this research question in several ways.

First, we propose a finer characterization of the instability of risk preferences, and a categorization of individuals as regard to the stability (or not) of their preferences towards risk. We observe that the sample is approximately equally split between individuals with stable preferences (42.81%) and with unstable ones (45.71%), weak (34.53%) and strong (11.18%). In addition, we observe that among individuals with unstable preferences, the weak instability largely dominates the strong one.

Second, we identify potential drivers for this instability that may be helpful for future research, in particular the strong impact of undereducation on the probability of instability. Third, we try to clarify what is behind the choice of Gamble 5 in the classic OLS procedure. Our results indicate that among those choosing Gamble 5 in the classic procedure, approximately 70% are risk loving, the others being risk neutral. In this sense, the classic procedure, by putting together individuals who are risk neutral and risk loving, does not allow a precise elicitation of individual preferences towards risk.

At first glance, one limitation of this paper is the difference in payoffs between our two elicitation procedures. However, it seems that this effect is negligiblz, and that our results are driven by the increase in the number of gambles from the classic OLS procedure to the extended one. Another potential limitation is the absence of monetary incentives. However, some papers show that this has no impact on the results [START_REF] Camerer | The effects of financial incentives in experiments: A review and capital-labor-production framework[END_REF][START_REF] Beattie | The impact of incentives upon risky choice experiments[END_REF][START_REF] Battalio | Testing between alternative models of choice under uncertainty: Some initial results[END_REF][START_REF] Wik | On the measurement of risk aversion from experimental data[END_REF]).

An interesting extension of this research could be a comparison of several existing elicitation procedures on the same sample, i.e. in a between-subject design. Such a comparison would be helpful in understanding the advantages and limits of measurements provided by such procedures, and to have a coherent and relevant use of these measurements to address research questions.

Part 3 of the questionnaire is composed with a choice experiment. In this part, it is indicated that forest provides a significant set of economic, social and environmental functions and benefits. However, due to its overuse, these functions may disappear in the future if nothing is done. Therefore, government agencies and NGOs consider the implementation of policies that will ensure the future supply of environmental goods and services. These policies may have an influence on people in your area. This study evaluates your preferences for different policies, knowing that they vary according to different attributes such as the biodiversity, the spiritual and cultural resources area, elephant population, forest landscape, and a potential individual compensation. The rest of the choice experiment is classic. Two blocks composed with 9 cards with different combinations of the attributes are proposed to the households.

  71 for Chinese farmers (Liu (2013)), around 0.8 for French farmers (Bocquého et al. (2014); Reynaud and Couture (2012); Bougherara et al. (2017)) and 0.69 for farmers in Burkina Faso (Cotty et al. (2014)).

Table 1 :

 1 Classic OLS procedure with 5 gambles

	Choice 50/50 gamble Payoff 1 Payoff 2 Coef. of RRA ranges	Risk profile
	Gamble 1	4	4	r > 2	Extremely risk averse
	Gamble 2	3	6	0.67 < r < 2	Highly risk averse
	Gamble 3	2	8	0.38 < r < 0.67	Very risk averse
	Gamble 4	1	10	0.20 < r < 0.38	Slightly risk averse
	Gamble 5	0	12	r < 0.20	Risk neutral/Risk loving
	Reynaud and Couture (2012) proposed an extended OLS procedure composed of nine gambles to
	allow for a finer characterization of risk loving preferences. Table 2 presents the procedure. The
	gambles 7, 8 or 9 correspond to different degrees of risk loving, from slightly to very risk loving. In
	the extended procedure, there are five categories for risk aversion, while only four are represented
	in the classic one. We can observe that "Risk averse" (choice of Gamble 4) and "Very risk averse"
	(choice of Gamble 3) in the extended procedure are gathered in "Very risk averse" gamble in the
	classic procedure. The households are always given Table 1 first, and then Table 2.

  procedure, 83 individuals choose Gamble 6 (i.e. 8.28% of the sample), and are therefore risk neutral, 692 chose gambles 1 to 5 (i.e. 69.07% of the sample) and are risk averse. Finally, 227 individuals choose gambles 7 to 9 (i.e. 22.65% of the sample) and are characterized as risk loving, which is approximately 1/4 of the sample.

Table 3 :

 3 Cross results of the classic and extended procedures

					Classic procedure
			Gamble 1 Gamble 2 Gamble 3 Gamble 4 Gamble 5 Total
	Extended procedure	Gamble 1 Gamble 2 Gamble 3 Gamble 4 Gamble 5 Gamble 6 Gamble 7 Gamble 8	270 31 13 6 6 5 2 2	21 63 30 33 23 15 5 5	18 18 24 22 37 34 13 7	5 5 9 10 9 20 18 20	4 11 5 8 11 9 10 13	318 128 81 79 86 83 48 47
		Gamble 9	6	14	12	8	92	132
		Total	341	209	185	104	163	1002

Table 4 :

 4 Descriptive statistics (N = 1002)

	Variables	Mean Std. Dev. Min Max
	Continuous
	Elephant density (number/hectare)	0.93	0.84	0.23 2.78
	Damage from HEC (*CFA 1000/years) 90.12	209	0	1200
	Land holding (in hectars)	4.48	5.30	0	56.25
	Access to credit (*CFA 1000/years)	46.81	351.75	0	9000.00
	Money transfer (*CFA 1000/years)	58.23	191.13	0	3000.00
	Baka employment	1.85	2.94	0	12
	Seniority (in years)	26.88	20.75	0	90.00
	Household size	6.45	4.02	0	20.00
	Age	48.40	14.61	16	90.00
	Dummy
	Reach secondary school	0.56	0.49	0	1
	Reliance on forest	0.71	0.45	0	1
	Community group (Yes = 1)	0.28	0.45	0	1
	Human-elephant-conflict (Yes = 1)	0.27	0.44	0	1
	Gender (Male = 1)	0.76	0.42	0	1
	Marital status (Married = 1)	0.72	0.45	0	1

Table 5 :

 5 Results of the binary probit regression (instability =1)We observe that individuals with higher financial assets, employ Baka autochtonous, reached sec-ondary school, as well as elder individuals are more likely to express stable risk preferences. Indeed, individuals with 1000 more CFA are associated with 0.11 less percentage point on their likelihood to express unstable risk preferences. Individuals employing one more Baka community members are 1.51 percentage point less prone to express unstable risk preferences. Older respondents and those who reached secondary school, are 0.52 and 11.35 percentage points less prone to express unstable risk preferences respectively.

		Estimate Std. Err. Marg. effects Sign.
	Land holding	-0.0562	0.0597	-0.0039
	Financial asset	-0.0156	0.0086	-0.0011 *
	Baka employment	-0.2153	0.1059	-0.0151 **
	Reliance on forest	6.1532	331.597	0.4306
	Community group	0.9398	0.4753	0.0658 **
	Seniority	0.0225	0.0133	0.0016 *
	Damage from HEC	0.0167	0.0089	0.0012 *
	Reach secondary school	-1.6216	0.467	-0.1135 ***
	Gender	0.3523	0.5289	0.0247
	Age	-0.0749	0.0223	-0.0052 ***
	(Intercept)	-4.0114	331.5981
	Log Lik (df=11)	-29.191
	AIC	80.383
	Significance level (p): *=10%, ** =5%, ***=1%.

We assume

2.5 and -2 as class midpoints for extreme ranges in the extended procedure and 2.5 and 0 in the classic one.

The purpose of a common initiative group of interest is to promote the economic and social development of members through the development of income-generating activities and to overcome the constraints faced by individual small-scale farmers[START_REF] Biénabe | The role of small scale producers' organizations to address market access[END_REF].

Acknowledgments

This work was supported by a Labex ARBRE innovative project "Risk Aversion, Livelihoods and Ecosystem Services Provisioning and Deforestation in Multifunctional Landscape (RESEL)". The UMR BETA is supported by a grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir" program (ANR-11-LABX-0002-01, Lab of Excellence AR-BRE). The University of Auburn is a collaborative partner of this work. Thanks to Pr. Dawoei Zhang for facilitating. The Center for International Forestry Research-Global Comparative Study (CIFOR-GCS) has contributed to the field work with funding provided by the Norwegian Agency for Development Cooperation (NORAD), grant n o : QZA-12/0882.

A Description of the questionnaire

The survey is about socioeconomic and ecological analysis of land uses in the Tridom complex. The answers provided are strictly confidential and will be analyzed for the writing of a doctoral thesis. This thesis aims to reflect on a diagram optimal planning that integrates social, economic and also concerns about conservation of biodiversity at the scale of the Tridom landscape. Please kindly give me some of your precious time to answer the questionnaire. By ensuring the confidentiality of your answers, we thank you in advance for your agreement. The questionnaire is composed of three parts and 30 pages.

Part 1 is dedicated to the choice determinants of land use and conversion. The first section deals with the socioeconomic characteristics of the household (age, gender, etc.) with 37 questions. The second section is about the autochthony and tribal affiliation (ethnic group, seniority in the village, etc.) with 7 questions. Third section tackles the land ownership and the nature of the land ownership and uses of forest land (non-timber forest product, property right, etc.) with 17 questions. Fourth section questions the conflict, land grabbing, overlapping and superimposition of user rights with 5 questions. Section fifth concerns transportation infrastructure and urbanization (road network, means of transport, etc.) with 4 questions. Section sixth questions the access to some basic services like access to water, electricity, etc. and also deals with housing characteristics. Section seven is interested in the health and education of the household's members while section eight questions the households about food safety. The last section is large and composed with 45 questions about the multifunctionality of the landscape: cultural value, tradition, conservation, spiritual and genetic value of the forest for people.

Part 2 of the questionnaire is dedicated to the measurement of the parameters of risk aversion.

---------------Dear participant, we stop the questionnaire for a short time and we propose to you a little game. More precisely, we propose to you two different tables composed of 5 gambles and 9 gambles respectively. For each table, you have to choose the gamble that you accept to play for given that each gamble is associated to two payoffs having 50% chance to occur each. ---------------


Benoit Bonnet
email: benoit.bonnet@inria.fr

Teddy Furon

Patrick Bas

Fooling an Automatic Image Quality Estimator

This paper presents our work on the 2020 MediaEval task: "Pixel Privacy: Quality Camouflage for Social Images". Blind Image Quality Assessment (BIQA) is an algorithm predicting a quality score for any given image. Our task is to modify an image to decrease its BIQA score while maintaining a good perceived quality. Since BIQA is a deep neural network, we worked on an adversarial attack approach of the problem.

INTRODUCTION

The internet is flooded with images. This is especially true with the growth of social networks over the last decade. All this data is used to perform analysis to bring out new trends or to train predictive models. When it comes to images, deep neural networks vastly lead the landscape of machine learning. These deep neural networks are especially known to thrive on big datasets. This leads to the idea that more data leads to better models. While there certainly is truth to that affirmation, better learning mostly comes out of better data. Good data is data that both fits the task (e.g. people, places, objects detection) and whose quality is good. Due to the amount of available data, a human could not perform this cherry-picking of good data. Automated classifiers like BIQA [START_REF] Hosu | KonIQ-10k: An Ecologically Valid Database for Deep Learning of Blind Image Quality Assessment[END_REF] have been trained to assess the quality of an image. This classifier was trained on images whose quality was labeled based on the perceived quality of the media (e.g. resolution, compression artifacts). To protect one's data, images can be manipulated and slightly modified to defeat the automatic quality assessment [START_REF] Liu | Exploring Quality Camouflage for Social Images[END_REF]. We chose an adversarial attack approach to achieve this goal.

APPROACH 2.1 Adversarial Examples

Adversarial examples were first introduced by Szegedy et al. [START_REF] Szegedy | Intriguing properties of neural networks[END_REF] in early 2014. They are usually studied in the case of image classification: An attack effectively crafts a perturbation of an image to a small extent but enough to fool even the best classifiers.

In this setup, an original image 𝑥 0 is given as an input to the trained neural network to estimate the probabilities ( p𝑘 (𝑥 0 )) 𝑘 of being from class 𝑘 ∈ {1, . . . , 𝐾 }. The predicted class is given by:

ĉ (𝑥 0 ) = arg max 𝑘 p𝑘 (𝑥 0 ). ( 1
)
The classification is correct if ĉ (𝑥 0 ) = 𝑐 (𝑥 0 ) the ground truth class for 𝑥 0 . The goal of an attack is to craft an imperceptible perturbation 𝑝 such that the adversarial sample 𝑥 𝑎 = 𝑥 0 + 𝑝 verifies ideally:

𝑥 ★ 𝑎 = arg min 𝑥: ĉ (𝑥)≠𝑐 (𝑥 0 ) ∥𝑥 -𝑥 𝑜 ∥, (2)
Where ∥ • ∥ is a measure of distortion, in most cases the Euclidean distance. A small distortion makes it less likely for human to perceive that the image was manipulated.

BIQA is a deep neural network and as such is vulnerable to adversarial attacks. However BIQA is not a classifier returning a class prediction but a regressor giving a quality score 𝐵𝐼𝑄𝐴(𝑥) ∈ [0, 100]. The notion of adversarial sample thus needs to be redefined. In our case, we set a target score 𝑠 𝑎 ∈ [0, 100]. Regardless of the original score 𝐵𝐼𝑄𝐴(𝑥 𝑜 ), our adversarial sample now ideally verifies:

𝑥 ★ 𝑎 = arg min 𝑥:𝐵𝐼𝑄𝐴(𝑥) <𝑠 𝑎 ∥𝑥 -𝑥 𝑜 ∥, (3)

Quantization

An original image 𝑥 0 in the spatial domain (e.g. PNG format) is a 3-dimensional discrete tensor: 𝑥 0 ∈ {0, 1, . . . , 255} 𝑛 (with 𝑛 = 3 × 𝑅 × 𝐶, 3 color channels, 𝑅 rows and 𝐶 columns of pixels). The main objective of this task is to craft images: 𝑥 𝑎 ∈ {0, 1, . . . , 255} 𝑛 . This additional constraint to the attack is yet not easy to enforce. In a deep neural network, this input image is first preprocessed onto a range domain that usually reduces variance of the data. Its purpose is to ease the learning phase and thus to increase the performance of a deep neural network. This preprocessing is defined by design before the training stage and cannot be modified at testing. In the case of BIQA, the range domain is [-0.5, 0.5] 𝑛 .

Most attacks of the literature are performed in this domain without consideration of the transformation it represents. This leads to an adversarial sample 𝑥 𝑎 ∈ [0, 255] 𝑛 after reverting the preprocessing. To save this adversarial sample 𝑥 𝑎 as an image, the first step is then to round it which will erase most of the perturbation in the case of a low-distortion attack. Rounding is therefore likely to remove the adversarial property of the sample.

Paper [START_REF] Bonnet | What If Adversarial Samples Were Digital Images?[END_REF] addresses this problem presenting a post-processing added on top of any attack to efficiently quantize a perturbation: It keeps the adversarial property while lowering the added distortion. The method is based on a classification loss to ensure adversariality defined as follows:

𝐿(𝑥) = log( p𝑐 (𝑥 0 ) (𝑥)) -log( p ĉ (𝑥) (𝑥)). (4)
To adapt this method to the context of BIQA, we only need to redefine it to:

𝐿(𝑥) = 𝐵𝐼𝑄𝐴(𝑥) -𝑠 𝑎 . (5)
For a given x, 𝐿(𝑥) < 0 ensures x scores under the target 𝑠 𝑎 .

MediaEval'20, December 14-15 2020, Online B. Bonnet, T. Furon, P. Bas

EXPERIMENTAL WORK

In this task, we know the classifier (BIQA) and its parameters. We are therefore in a white-box setup. Most modern attacks are developed in this scenario, from the most basic FGSM [START_REF] Goodfellow | Explaining and Harnessing Adversarial Examples[END_REF] and IFGSM [START_REF] Kurakin | Adversarial Machine Learning at Scale[END_REF] to the most advanced PGD [START_REF] Madry | Towards Deep Learning Models Resistant to Adversarial Attacks[END_REF], C&W [START_REF] Carlini | Towards evaluating the robustness of neural networks[END_REF], BP [START_REF] Zhang | Walking on the Edge: Fast, Low-Distortion Adversarial Examples[END_REF]. FGSM is a noniterative attack bringing a fast solution of the problem. Our work used this attack in the early stages as a proof of concept bringing a quick further understanding of the problem. Artifacts were visible. Instead all the results reported here are crafted using more the advanced PGD attack [START_REF] Madry | Towards Deep Learning Models Resistant to Adversarial Attacks[END_REF] in its 𝐿 2 optimization version. One input parameter is the distortion budget. We run the attack over 7 iterations with different distortion budgets (whose maximum value is set to 2000). A binary search quickly finds an adversarial sample with the lowest distortion.

JPEG compression

The final images will be evaluated on their JPEG [START_REF] Wallace | The JPEG still picture compression standard[END_REF] counterpart. This compression is done with a quality factor of 90. However there are many image compression sofwares providing different results. We used the command line $ convert to simulate this compression. Tables 1 and2 show for different methods both 𝑃 𝑃 𝑁 𝐺 and 𝑃 𝐽 𝑃𝐸𝐺 respectively the percentage of images successfully beating the target score in the PNG domain and the JPEG domain. Additionally Table 2 shows results of the jury as well.

Quantization

Spatial domain.

The work [START_REF] Bonnet | What If Adversarial Samples Were Digital Images?[END_REF] serves as a baseline for quantization. We only slightly adapt it as stated in Sect. 2.2. Table 1 reports our results for two target scores: 𝑠 𝑎 = 30 and 𝑠 𝑎 = 50. It appears that the perturbation crafted in the pixel domain is fragile when facing a JPEG compression.

DCT domain.

The final image being evaluated after a JPEG compression, we explore a method adapting the quantization [START_REF] Bonnet | What If Adversarial Samples Were Digital Images?[END_REF] to the DCT domain. Using the same notations [START_REF] Bonnet | What If Adversarial Samples Were Digital Images?[END_REF]: Let 𝑋 𝑜 denote the image in the DCT domain, 𝑋 𝑎 = 𝑋 𝑜 + 𝑃 is the result of an initial attack like PGD, and 𝑋 𝑞 = 𝑋 𝑜 + 𝑃 + 𝑄 the final quantized transformed coeffcients. We solve a Lagrangian formulation:

𝑋 𝑞 = 𝑋 𝑜 + 𝑃 + arg min 𝑄 𝐷 (𝑄) + 𝜆𝐿(𝑄), (6)
where 𝜆 is the Lagrangian multiplier controlling the tradeoff between the distortion 𝐷 (𝑄) and 𝐿(𝑄) defined in [START_REF] Kurakin | Adversarial Machine Learning at Scale[END_REF]. The distortion 𝐷 (𝑄) is defined as the squared 𝐿 2 norm of added perturbation:

𝐷 (𝑄) = ∥Δ × (𝑃 + 𝑄)∥ 2 .
The quantization noise 𝑄 is s.t. 𝑋 𝑜 + 𝑃 + 𝑄 ∈ ΔZ 𝑛 , where Δ ∈ N 𝑛 is the quantization step matrix for JPEG QF=90. If we use a first order approximation of 𝐿(𝑄), we can develop (6) in a second-degree polynomial function. For any coefficient 𝑗, this function is locally minimized by:

𝑄 ★ ( 𝑗) = -𝑃 ( 𝑗) -𝜆 𝐺 ( 𝑗) 2Δ( 𝑗) , (7)
where 𝐺 = ∇𝐿(𝑄)| 𝑄=0 the gradient computed at 𝑄 = 0. This minimum however does not enforce (𝑃 + 𝑄 ★ ) ∈ Z 𝑛 . A simple rounding of (𝑃 + 𝑄) will then finalize the quantization. Finally we need to control a maximum allowed distortion. If 𝜆 gets big, 𝑄 ( 𝑗) become a very high value which is not desirable. The final value

RESULTS AND ANALYSIS

Tables 1 and2 show the importance of considering the JPEG compression. When the image is quantized by the 𝐿 2 optimization in the spatial domain, most images will successfully be adversarial images. However, very few of them remain adversarial after the JPEG compression. The BIQA score on most images increases up to 10 points. If the quantization is done in the DCT domain, most of them remain adversarial and the task is successful. It is however obviously more difficult to beat a lower target score 𝑠 𝑎 . An interesting property of the DCT quantization is that it creates typical JPEG artifacts as seen on Figure 1. This is especially true in low frequency images since it is harder to remain undetectable in a such situation.

DISCUSSION AND OUTLOOK

The MediaEval task was a good opportunity to extend our previous work [START_REF] Bonnet | What If Adversarial Samples Were Digital Images?[END_REF] to 1) a regressor BIQA, and 2) in the DCT domain. Saving the DCT coefficients directly into a JPEG image is more consistent as it offers a better control on adversariality. Another difficulty of this task was the lack of knowledge about the compression algorithm. We therefore worked in a 'gray' box setup. The results showed that JPEG compression have a big effect on the BIQA score of, at least, adversarial images (and probably any other quality estimator). Hopefully our JPEG compression is close to the one used in the contest which allowed transferability of our adversarial images.

Table 1 :

 1 Probabilities of success with a spatial Quantization 𝑃 𝑃 𝑁𝐺 𝑃 𝐽 𝑃𝐸𝐺 𝑠 𝑎 = 30 99.0% 0.7% 𝑠 𝑎 = 50 100.0% 11.1%

Table 2 :

 2 Probabilities of success with a DCT Quantization 𝑃 𝑃 𝑁𝐺 𝑃 𝐽 𝑃𝐸𝐺

	Accuracy	Number of times
	after(JPEG90)	selected "best"

Δ ]. These images were submitted to the jury.


domain: spi phys info math

text:
Alexis Lechat
email: alexis.lechat@onera.fr

Stéphane Herbin
email: stephane.herbin@onera.fr

Frédéric Jurie
email: frederic.jurie@unicaen.fr

Adaptation du problème de questions-réponses visuelles à un contexte d'apprentissage continu

Le problème de questions-réponses visuelles (QRV) constitue un nouveau défi en intelligence artificielle. Il requiert du système des capacités de raisonnement alliant compréhension visuelle et linguistique. Nous proposons d'adapter le problème QRV à une configuration d'apprentissage continu, paradigme dont l'objectif est de créer des modèles capables d'apprendre et de s'adapter dans un environnement évolutif. L'étude réalisée ici s'intéresse à un protocole d'apprentissage séquentiel de tâches définies via un partitionnement sémantique des questions. Ce protocole est analysé sur un modèle QRV courant combiné à une solution incrémentale de répétition sur mémoire épisodique.

Abstract -Visual question answering (VQA) is one of the new challenge for artificial intelligence. It is a complete task since it requires reasoning skills combining both visual and linguistic knowledge. In this paper, we provide a way to train a VQA model in a continuous learning setting, a paradigm suitable for incrementing the knowledge of adaptive systems evolving in a changing environment. We define a task incremental protocol whose tasks are built on a semantic question clustering. This method is accredited on a common VQA model combined with an episodic memory for rehearsal learning.

Introduction

Les réseaux de neurones profonds constituent l'état de l'art de nombreux problèmes de vision par ordinateur. Les meilleures performances sont généralement obtenues en suivant un paradigme particulier : une phase d'apprentissage et une phase de validation. Le réseau résultant est ainsi spécialisé au domaine défini par les données d'apprentissage. L'une des principales faiblesses de ce schéma de conception est la difficulté à étendre les compétences initiales du réseau, par exemple par l'ajout de nouvelles classes à discriminer. L'apparition d'un phénomène couramment dénommé oubli catastrophique [START_REF] Goodfellow | An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks[END_REF], i.e. le fait que de nouvelles données ou tâches puissent provoquer l'oubli de ce qui a été appris antérieurement, pose problème.

Une solution immédiate serait de ré entraîner complètement un réseau à partir d'une base intégrant les nouvelles données. Dans de nombreuses applications, cependant, le système exploitant le réseau évolue dans un environnement réel et doit absorber un flux continu. Il apparaît donc utile de disposer d'un modèle capable de s'adapter aux variations de son milieu et d'apprendre à partir de nouvelles expériences sans dégrader ses acquis. C'est l'enjeu de l'apprentissage incrémental ou apprentissage continu qui cherche à contrôler l'oubli catastrophique, mais aussi à favoriser les transferts entre nouveaux savoirs et connaissances apprises afin d'accélérer le processus d'entraînement tout en renforçant progressivement les performances globales.

Une application de questions-réponses visuelles (QRV) [START_REF] Antol | Visual Question Answering[END_REF] consiste à répondre à une question en langage naturel sur le contenu d'une image. Ce problème est par nature multimodal, car il requiert du système un raisonnement sur des connaissances à la fois visuelles et linguistiques [START_REF] Johnson | Inferring and Executing Programs for Visual Reasoning[END_REF], et multitâches, car il implique des capacités de classification, de détection d'objet ou d'attribut, de localisation, de comptage, etc.

L'augmentation du nombre de données QRV accessibles [START_REF] Hudson | GQA: a new dataset for compositional question answering over real-world images[END_REF] suscite l'intérêt pour un système dont la connaissance puisse s'incrémenter. En particulier, il semble naturel qu'un système QRV rencontre, au cours de son existence, de nouveaux contextes visuels, de nouveaux termes de vocabulaire ou de nouvelles tournures grammaticales.

La contribution de cet article est d'introduire un schéma d'apprentissage incrémental sur un système QRV. Nous proposons notamment de simuler l'incrémentation du nombre de tâches réalisables par le modèle par un partitionnement sémantique des questions. Nous évaluons ce protocole sur l'ensemble VQAv2 [START_REF] Goyal | Making the V in VQA Matter: Elevating the Role of Image Understanding in Visual Question Answering[END_REF].

Travaux connexes 2.1 Gérer l'oubli catastrophique

Les approches d'apprentissage continu dans la littérature se focalisent sur la maîtrise de l'oubli catastrophique. Trois catégories de stratégies ont été proposées : -Architecture adaptative : l'architecture même du réseau est modifiée pour traiter l'oubli. Une approche courante est d'agrandir progressivement le réseau pour augmenter sa capacité [START_REF] Rusu | Progressive Neural Networks[END_REF].

-Régularisation : la fonction de coût est contrainte pour consolider les poids liés aux connaissances apprises, par exemple la méthode de l'"Elastic Weight Consolidation" [START_REF] Kirkpatrick | Overcoming catastrophic forgetting in neural networks[END_REF]. -Répétition : une mémoire épisodique sauvegarde une partie de l'information rencontrée pendant l'apprentissage. Cette information est exploitée et mise à jour périodiquement afin de renforcer les connaissances apprises lors de l'entraînement sur de nouveaux exemples (e.g. iCaRL [START_REF] Rebuffi | iCaRL: Incremental Classifier and Representation Learning[END_REF]). L'apprentissage continu est un sujet récent et les protocoles d'évaluations sont en voie d'uniformisation [START_REF] Parisi | Continual Lifelong Learning with Neural Networks: A Review[END_REF]. Les applications se limitent encore principalement à des contextes simples (classification sur un faible nombre de classes) et à des ensembles de données restreints (MNIST, CIFAR, CORe50).

Les différents types d'apprentissage continu

L'apprentissage continu repose sur la façon dont est organisé le flux entrant de données. On suppose que la base d'apprentissage s'incrémentera tout au long de la vie du modèle, mais sans a priori sur la quantité, la dimension, ou la distribution des données ou sur le nombre de classes.

Plusieurs approches sont utilisées pour simuler un flux de données. Parmi les plus communes [START_REF] Parisi | Continual Lifelong Learning with Neural Networks: A Review[END_REF][START_REF] Hsu | Re-evaluating Continual Learning Scenarios: A Categorization and Case for Strong Baselines[END_REF], on retrouve :

-incrémentation de classes : le réseau apprend successivement sur toutes les instances d'une classe avant d'avoir accès à la suivante, et ne reverra plus les anciennes. -incrémentation de tâches : les données sont ordonnées en tâches apprises séquentiellement par le réseau. -incrémentation de domaines : cela correspond à apprendre sur des données dans un nouveau domaine de représentation comparé à ce qui a déjà été vu (e.g. passer d'images réelles à des images artistiques...). Dans la section suivante, nous discutons des particularités du QRV lors de la mise en place d'un protocole incrémental avant de proposer une méthode de partitionnement des données pour une approche d'incrémentation de tâches.

QRV incrémental 3.1 Organisation des données pour le QRV

Les données se présentent sous la forme de triplets (Image, Question, Réponse) (noté (v, q, a)). On travaille ici avec le jeu de données VQAv2 (Figure 1).

À partir de cet ensemble, comme mentionné dans la section précédente, plusieurs logiques sont possibles pour simuler un flux continu de données. En se ramenant à un problème de classification (une réponse correspond à une classe), en associant chaque question à une tâche ou en répartissant les images par domaine, il est possible d'envisager l'une des approches incrémentales classiques. Cependant, le format multimodal des données permet également de définir d'autres variantes spécifiques au QRV.

Nous proposons d'étudier dans ce travail un partitionnement sémantique des questions comme logique de structuration du flux de données. L'idée sous-jacente est de simuler un ap-Figure 1 -Exemples de l'ensemble VQAv2 [START_REF] Goyal | Making the V in VQA Matter: Elevating the Role of Image Understanding in Visual Question Answering[END_REF].

prentissage incrémental de tâches complexes d'interprétation visuelle, et d'étudier la capacité des algorithmes à le réaliser.

Partitionnement sémantique des questions

Les types de tâches étant très dépendants de certains termes tels que les mots interrogatifs, un partitionnement sémantique regroupe naturellement les questions concernant des tâches similaires. On simule ainsi un problème d'apprentissage séquentiel de diverses tâches comme le dénombrement, la détection d'attribut ou la vérification d'existence.

Afin d'obtenir un résultat équilibré, nous proposons de réaliser le partitionnement des questions sur un critère de distance après plongement sémantique. On utilise pour cela la représentation GloVe [START_REF] Pennington | GloVe: Global Vectors for Word Representation[END_REF] qui à chaque mot associe un vecteur de dimensions 300. Chaque question est encodée en un unique vecteur de dimension 300 en moyennant sur l'ensemble des mots qui la compose.

On considère l'union des questions d'entraînement et de validation (215 723 questions différentes). On obtient ainsi notre subdivision en tâches pour l'apprentissage ainsi que les différents sous-ensembles de validation spécifiques à chaque tâche. Dans nos expérimentations, la base VQAv2 est partitionnée en 20 tâches via un algorithme des K-moyennes utilisant la distance euclidienne.

Bien que simple, cette méthode permet d'obtenir des tâches sémantiquement homogènes. Les premiers mots de la question sont les plus déterminants lors du partitionnement. Par exemple, toutes les questions commençant par "Is there..." sont regroupée dans la même tâche, de même pour les questions débutant par "What is the..." ou "Does the [...] have...", ceci étant notamment dû à la fréquence prédominante de ces termes dans le corpus. Néanmoins, l'encodage GloVe permet aussi un regroupement lexical pertinent.

Expérimentations

Modèle de prédiction de réponse

Dans le cadre de notre étude, on s'intéresse principalement au comportement d'un modèle QRV dans un contexte d'apprentissage continu. On utilise pour cela un modèle générique inspiré de l' état de l'art QRV [START_REF] Anderson | Bottom-Up and Top-Down Attention for Image Captioning and Visual Question Answering[END_REF] auquel on peut ajouter Figure 2 -Chaîne de traitement du modèle QRV de fusion multimodal utilisant des descripteurs visuels globaux [START_REF] Anderson | Bottom-Up and Top-Down Attention for Image Captioning and Visual Question Answering[END_REF].

une mémoire épisodique pour mettre en place une stratégie de répétition.

Ce modèle est constitué de deux branches, l'une encodant l'information visuelle contenue dans les images à partir de caractéristiques profondes (ResNet) apprises sur la base ImageNet, l'autre encodant la sémantique des questions à partir d'un réseau récurrent (GRU). Ces deux branches sont ensuite combinées par produit pour prédire la réponse, considérée comme la sortie d'un classifieur (Figure 2).

Ce modèle associant des encodages multimodaux et des mécanismes de fusion est typique de la plupart des approches proposées dans la littérature, dans son architecture et ses composants. Il est utilisé dans notre étude comme référence pour révéler les phénomènes caractéristiques d'un apprentissage incrémental de tâches de QRV.

Le modèle implémenté ici atteint une précision de 53% sur la validation du VQAv2 lors d'un entraînement en batch standard.

Évaluation sur le partitionnement par question du VQAv2

Le protocole suivi dans nos expérimentations est le suivant. Chaque tâche est montrée au réseau de manière séquentielle.

Celui-ci réalise une unique passe d'apprentissage ("epoch") sur le sous-ensemble avant de passer à la tâche suivante. De manière similaire au protocole proposé dans [START_REF] Maltoni | Continuous Learning in Single-Incremental-Task Scenarios[END_REF], on étend le nombre de sorties possibles du classifieur prédisant les réponses au fur et à mesure que de nouvelles classes/réponses sont rencontrées. Trois types d'approches sont évaluées. Dans une première, on s'intéresse à un modèle entraîné naïvement sur les 20 tâches consécutives sans modification des paramètres d'apprentissage. Aucune solution n'est mise en place pour lutter contre l'oubli catastrophique.

Une deuxième approche exploite une mémoire épisodique de taille prédéfinie M qui accumule une partie des données observées. À chaque nouvelle tâche, le modèle apprend à la fois sur les nouveaux échantillons et sur ceux stockés en mémoire. Le nombre d'éléments conservés est équilibré entre les tâches : à la n-ième tâche, la mémoire stocke au plus M n triplets (v, q, a) par tâche observée. La sélection des éléments à mémoriser est aléatoire. Nous avons testé pour M = 4000 et M = 40000 ce qui correspond environ à 1% et 10% du nombre total de données d'entraînement (443 757). Cette approche simple de mémorisation montre des performances équivalentes, voire supérieures à d'autres méthodes (régularisation, intelligence synaptique) sur des problèmes d'incrémentation de classes [START_REF] Hsu | Re-evaluating Continual Learning Scenarios: A Categorization and Case for Strong Baselines[END_REF].

On évalue aussi la performance obtenue dans le cas d'une répétition totale. Cette configuration correspond à une mémoire de taille infinie permettant de sauvegarder la totalité des don-Figure 3 -Évolution de la précision en fonction du nombre de tâches vues. Les modèles sont testés sur un ensemble de validation qui s'incrémente au fil des tâches.

nées vues pour les repasser au réseau à chaque nouvelle tâche. Cela nous donne la borne supérieure atteignable par un apprentissage incrémental avec répétition sur une mémoire épisodique.

Résultats

L'entraînement des 4 modèles est optimisé avec la méthode de descente de gradient stochastique. Le taux d'apprentissage est fixé à 0.1 et reste constant. Nous n'avons pas choisi de méthode de pas adaptatif pour l'optimisation (Adam, Adamax, RMSProp, etc.) pour mieux révéler les phénomènes.

À la tâche n, on évalue le réseau sur l'ensemble de validation composé de l'union des sous-ensembles associés aux tâches 1 à n. La mesure de précision utilisée est celle définie pour le challenge VQA [START_REF] Antol | Visual Question Answering[END_REF].

Les résultats sont disponibles en Figure 3. Le modèle sans répétition montre un phénomène d'oubli particulier. La performance globale du réseau se dégrade avec l'ajout de tâche, comme attendu dans ce contexte incrémental. Cependant, on constate que certaines tâches provoquent un oubli catastrophique violent. Le faible score à ces itérations prouve qu'en plus d'oublier les anciennes tâches, le réseau n'arrive pas à apprendre la nouvelle. La performance est cependant capable de remonter à la tâche suivante. Cela s'explique par la forte corrélation entre certaines tâches du problème de QRV et à notre partitionnement.

En effet, le VQAv2 est constitué à plus de 40% de questions fermées (classes "Yes" et "No"). La distribution des questions ouvertes est très hétérogène et une grande partie des réponses ont moins de dix exemples. On retrouve ce biais dans notre partitionnement avec les tâches 7, 8, 11 et 15 qui comportent principalement des questions "What..." alors que les 14 et 16 sont des tâches liées au dénombrement: "How many...". Le reste des tâches comporte une plus grande proportion de questions fermées. C'est la cause principale des oscillations de la précision. Le réseau est capable d'apprendre rapidement la classification binaire oui/non et cela se répercute par un gain de performance sur l'ensemble des tâches contenant des questions fermées. Cependant, une tâche composée uniquement de classes rares provoque un oubli brutal de la connaissance acquise du modèle. La permutation de l'ordre des tâches pendant l'apprentissage n'impacte pas le résultat observé : ce sont les mêmes tâches qui provoquent une chute des performances.

L'ajout d'une mémoire épisodique stabilise le comportement du réseau et augmente ses performances proportionnellement à sa taille.

La Figure 4 montre l'évolution de la précision du modèle sur 4 tâches tout au long de son cycle de vie. La forte corrélation inter tâche, en particulier pour les questions fermées, est ici aussi illustrée par la précision élevée du réseau sur des tâches qu'il n'a pas encore rencontrées (par exemple, la tâche 6). D'autre part, la comparaison entre le modèle sans mémoire et celui avec une mémoire de taille 40 000 met clairement en valeur l'impact de la répétition. Les tâches sur lesquelles le réseau performe correctement voient leur précision se stabiliser et le modèle réussit à s'améliorer sur les tâches les plus difficiles dont les résultats étaient négligeables dans le cas sans mémoire.

Conclusion

La diversité et la complexité du problème QRV motivent l'intérêt de disposer d'un modèle capable d'apprendre de façon continue. Dans cet article, nous avons proposé une démarche d'évaluation incrémentale reposant sur un partitionnement sémantique des questions. Cette méthode permet d'organiser le flux de données d'apprentissages en tâches qui sont montrées au modèle de manière séquentielle et de comparer les performances des algorithmes.

L'étude réalisée ici sur la base VQAv2 permet d'illustrer les spécificités du QRV par rapport aux problèmes de classification usuellement utilisés dans la littérature de l'apprentissage continu. Les différents niveaux de corrélation entre tâches ont un impact important sur les performances. Il peut être positif -certaines tâches profitant des apprentissages passés -, mais également fortement négatif et provoquer un oubli catastrophique global sur les tâches anciennes. Des méthodes simples exploitant une mémoire épisodique permettent de limiter ces phénomènes.

Pour la suite de nos travaux, nous nous intéressons à d'autres démarches pour le partitionnement des tâches (en prenant en compte par exemple le domaine visuel) pour analyser le comportement de l'apprentissage continu, et conduire à de nouvelles méthodes pour contrôler l'oubli catastrophique des modèles de QRV.

Figure 4 -

 4 Figure 4 -Comparaison de l'évolution de la précision pour 4 tâches différentes entre un modèle sans mémoire (à gauche) et le modèle avec une mémoire de taille 40 000 (à droite). Chaque tâche voit sa précision mesurée sur son ensemble de validation propre.