Manh Hung Pham

Jean-Dominique Durand

Minh Phong Le

| Bich

Thao T Vo

| Duc

Huy Hoang

Jacques Panfili

Thao T Bich

Vo

Huy Duc

Hoang

Importance of various marine coastal habitats during the life cycle of Spratelloides delicatulus in Con Dao, the oldest MPA in Vietnam

Keywords: Clupeidae, conservation, coral reef, growth, otolith, seagrass ORCID

1. Marine protected areas (MPAs) are set up to conserve biodiversity, but their design is not always based on strictly scientific considerations. Ideally, an MPA should protect all key habitats necessary for a marine species to complete its life cycle. The identification of these key habitats is complex, especially during the early life of marine fishes.

2. A widely distributed tropical and important low trophic-level fish species, Spratelloides delicatulus (Clupeidae), was used to evaluate the significance of various coastal habitats for its larvae and juveniles in the Con Dao Archipelago MPA in Vietnam. Early stages (larvae and juveniles) were sampled monthly over one year (June 2016 to May 2017) using light traps in three main habitats (seagrass beds, coral reefs and harbour). The species was identified using morphometry and DNA barcoding. Age and growth variables were estimated using otolith daily growth increments.

3. A total of 3,581 fish were caught. The species was not found in captures between January and February, directly linked to the decrease in seawater temperature and was most abundant from April to June. For a subsample of 248 fish (7-38 mm standard length), ages ranged from 7 to 108 days.

4. Captures and back-calculated birthdates using otolith daily increments showed that S. delicatulus spawns during the period of high seawater temperature, from March to October. The species colonizes all three habitats during the early stages (0-26 days old), with growth rate lowest on the seagrass beds. Nevertheless, the species occupies seagrass beds exclusively during the older stages.

5. The conservation of seagrass beds in the Con Dao archipelago is essential for protection of juvenile stages of this species but this habitat is presently not included in the MPA patches. Establishment of a continuum of protected areas linking habitats, rather than the existing patches is needed to conserve the complete life cycle of this species in the Con Dao MPA.

| INTRODUCTION

Marine protected areas (MPA) are considered effective instruments to help mitigate the loss of marine biodiversity, including restoration of intensively fished stocks [START_REF] Hiscock | The role of marine protected areas for biodiversity conservation and for science[END_REF] and protection of particular key habitats [START_REF] Bailey | Using marine mammal habitat modelling to identify priority conservation zones within a marine protected area[END_REF][START_REF] Evans | Combined application of biophysical habitat mapping and systematic conservation planning to assess efficiency and representativeness of the existing High Seas MPA network in the Northeast Atlantic[END_REF]. In tropical regions, coastal marine habitats such as seagrass beds, coral reefs and mangroves are considered to be nurseries for juvenile stages of many species [START_REF] Igulu | Mangrove habitat use by juvenile coral reef fish: Meta-analysis reveals that tidal regime matters more than biogeographic region[END_REF][START_REF] Minello | Salt marshes as nurseries for nekton: Testing hypotheses on density, growth and survival through meta-analysis[END_REF][START_REF] Nagelkerken | Importance of mangroves, seagrass beds and the shallow coral reef as a nursery for important coral reef fishes, using a visual census technique[END_REF], thus, the protection of these habitats is essential. The Con Dao archipelago houses the oldest MPA in Vietnam, established in 1984 to conserve essential habitats, not for fisheries but for dugong (Dugon dugong), blue whales (Neophon phocaenoides), Irrawaddy dolphin (Orcaella brevirostris), green turtle (Chelonia mydas) and hawksbill sea turtle (Eretmochelys imbricata). Therefore, this MPA focuses on protecting a few patches of coastal waters (Figure 1) which correspond to separated habitats (mainly coral reefs and a few seagrass beds) where these threatened or endangered species are present. Fishing is still active in the different habitats of this MPA. The roles and functions of the various habitats in fish life cycles are unknown in this area, in particular, the use of habitats by early life stages of various fish species and habitat connectivity during the fish life cycle.

The blue sprat Spratelloides delicatulus (Bennett, 1832) is a lowtrophic-level fish species, and important prey for many predators such as Lutjanus vitta, Auxis thazard, Megalaspis cordyla and Scomberoides lysan [START_REF] Blaber | Diets of lagoon fishes of the Solomon Islands: Predators of tuna baitfish and trophic effects of bait fishing on the subsistence fishery[END_REF]. It is abundant along the Vietnamese coasts [START_REF] Le | A checklist of the herrings (order: Clupeiformes) in the Vietnamese marine waters[END_REF] and more generally in the Indo-Pacific Ocean, from Southeast Africa to Southern Japan and Southern Australia [START_REF] Whitehead | Clupeoid fishes of the world (suborder Clupeoidei)[END_REF]. This species is important in live-bait fisheries in the Solomon Islands, the Maldives and the Laccadive Sea (India) [START_REF] Pillai | Exploited and potential resources of live-bait fishes of Lakshadweep[END_REF][START_REF] Milton | Age and growth of major baitfish species in Solomon Islands and Maldives[END_REF]).

In the recent past, over-exploitation of this species was reported after the introduction of mechanized vessels in the pole and line tuna fishery, with demand exceeding the stock capacity [START_REF] Pillai | Exploited and potential resources of live-bait fishes of Lakshadweep[END_REF].

Although the IUCN status of this species is least concern (LC), research on its life history and ecology is needed in the current context of its exploitation [START_REF] Santos | Spratelloides delicatulus. The IUCN Red List of Threatened Species 2017[END_REF]. In Vietnam, S. delicatulus is exploited in most coastal waters, including the Con Dao MPA, because it is one of the six species included in the production of fish sauce [START_REF] Chabanaud | Inventaire de la faune ichyologique de l'Indochine, lère liste[END_REF][START_REF] Pham | Characteristics and chemical composition of Vietnamese fish sauce[END_REF]. It also has a great value as 'pickled anchovy' and is used as bait for tuna fishing. It is a shortlived species, with a lifespan which does not exceed more than 5-6 months [START_REF] Milton | Age and growth of three species of tuna baitfish (Genus: Spratelloides) in the tropical Indo-Pacific[END_REF]. During its short life, it is found in various different marine coastal habitats such as coral reefs, lagoons and seagrass beds (Milton et al., 1991). S. delicatulus becomes sexually mature at 60-65 days old and then grows slowly (Milton et al., 1990;Milton et al., 1991;[START_REF] Milton | Age and growth of three species of clupeids from Kiribati, tropical central south Pacific[END_REF]. Some studies have reported variation in age and growth of S. delicatulus in coral reefs and coastal lagoon habitats in the Pacific and Indian Oceans (Milton et al., 1990;Milton et al., 1991;[START_REF] Milton | Age and growth of three species of clupeids from Kiribati, tropical central south Pacific[END_REF]. Although this species is abundant in seagrass beds (Milton et al., 1991), it is not known if these habitats are optimal for growth. In addition, there is very limited information on early stages and the life cycle of this species (Milton et al., 1990;Milton et al., 1991;[START_REF] Milton | Age and growth of three species of clupeids from Kiribati, tropical central south Pacific[END_REF]. S. delicatulus smaller than 15 mm have not been studied [START_REF] Conand | Biology of the small pelagic fishes of the lagoon of New Caledonia used as bait fish for tuna fishing[END_REF][START_REF] Dalzell | gracilis (Apogonidae) from Fijian waters. Tuna and Billfish Assessment Programme[END_REF]Milton et al., 1991;[START_REF] Milton | Age and growth of three species of clupeids from Kiribati, tropical central south Pacific[END_REF][START_REF] Milton | Fecundity and egg production of four species of short-lived clupeoid from Solomon Islands, tropical South Pacific[END_REF][START_REF] Milton | Recruitment patterns and factors affecting recruitment of five species of short-lived clupeid in tropical South Pacific[END_REF]; FIGURE 1 Map of the Con Dao MPA showing the five sampling sites in Con Son Bay: seagrass 1 (dark green dot), seagrass 2 (light green dot), coral reef 1 (dark blue dot), coral reef 2 (light blue dot) and harbour (orange dot) [START_REF] Mohan | Biology of the baitfishes Spratelloides delicatulus (Bennet) and S. japonicus (Houttuyn) from Minicoy waters[END_REF] because the identification of Clupeiformes larvae is challenging with uncertain morphology which changes rapidly during early stages [START_REF] Ko | Evaluating the accuracy of morphological identification of larval fishes by applying DNA barcoding[END_REF][START_REF] Victor | Identification of the larval and juvenile stages of the cubera snapper, Lutjanus cyanopterus, using DNA barcoding[END_REF]. In this context, a better understanding of spatial and growth dynamics of S. delicatulus is needed to clarify the importance of the various habitats during its life cycle, and specifically at the beginning of its life.

DNA barcoding is becoming more widely used as a tool for identifying larval fishes rapidly and efficiently, replacing conventional morphological methods [START_REF] Collet | DNA barcoding post-larvae can improve the knowledge about fish biodiversity: An example from La Reunion, SW Indian Ocean[END_REF][START_REF] Ko | Evaluating the accuracy of morphological identification of larval fishes by applying DNA barcoding[END_REF]. The present study identified early stages of S. delicatulus from very diverse ichthyoplankton samples using DNA barcoding coupled with morphometry, to determine its pattern of habitat occupation using spatial and temporal sampling. The study sought to provide information about the life history of this species in the Con Dao MPA as well as:

(a) determine the distribution of S. delicatulus in different habitats (seagrass beds, coral reefs and a harbour) during early stages using monthly sampling with light traps; (b) estimate the ages and variable growth across habitats by analysing otolith growth increments;

(c) discuss the colonization and survival of S. delicatulus in the various habitats; and (d) provide recommendations on key habitats for conservation. This is the first study in the Con Dao MPA to improve the conservation of an important low-trophic-level and prey fish species, targeted by specific fisheries.

| MATERIALS AND METHODS

Early life S. delicatulus were caught in three different marine coastal habitats in the Con Dao Archipelago: seagrass beds, coral reefs and a harbour. Two sites were chosen in seagrass beds and coral reefs, and one in the only harbour closely connected to the seagrass and coral reef sites (Figure 1): seagrass 1 (8 41 0 05.9 00 N 106 37 0 52.1 00 E), seagrass 2 (8 41 0 11.7 00 N 106 38 0 34.0 00 E), coral reef 1 (8 39 0 55.0 00 N 106 39 0 33.1 00 E), coral reef 2 (8 40 0 10.7 00 N 106 37 0 13.4 00 E) and harbour (8 40 0 36.6 00 N 106 36 0 19.3 00 E). All of these sites were in Con Son Bay. Fish were collected monthly for one year at the new moons, from June 2016 to May 2017, except for August 2016 owing to the loss of collection equipment at sea. The samples were taken using four 5 L light traps at each site during the whole night. Because fish are sensitive to different light wavelengths depending on the species or ontogenetic stage [START_REF] Bowmaker | The visual pigments of fish[END_REF][START_REF] Fitzpatrick | Using artificial illumination to survey nocturnal reef fish[END_REF], two types of light traps were used at each sampling site: two with two LED lights (3 W), and two others with four LED lights (3 W) to attract different fishes. Three Panasonic 3,400 mAh Li-ion batteries were used for each light trap to ensure that the lights worked all night. The light traps were set at 3-5 m deep from 6:00 p.m. to 4:00 a.m. (10 h). The contents of each light trap were collected early in the morning. Fish were killed by placing on ice and then stored preserved in 1 L containers filled with 99% ethanol. While the light traps were in place, the environmental parameters (temperature, salinity) were recorded from the sea surface to the bottom using a Castaway CTD probe (four times at each sampling site).

Fish from each light trap were sorted in the laboratory by morphology as described by [START_REF] Leis | Leiden and the Fauna Malesiana Foundation All[END_REF]. The samples from each light trap that were identified as Spratelloides spp. were sorted according to morphotypes. At least one specimen of each morphotype was selected for DNA barcoding using a 650 bp fragment of the mitochondrial cytochrome c oxidase I gene (COI), which was considered relevant for identification at the lowest taxonomic level [START_REF] Ko | Evaluating the accuracy of morphological identification of larval fishes by applying DNA barcoding[END_REF]. DNA was extracted from muscle tissue using the NucleoMag 96 Tissue kit (Macherey-Nagel). A fragment of approximately 650 bp of the mitochondrial DNA COI gene was amplified using the primers FishF1 and FishF2 in combination with FishR1 [START_REF] Ward | DNA barcoding Australia's fish species[END_REF]. The 25 ml PCR reaction mixtures comprised 7.5 μl of ultrapure water, 12.5 μl 2X Tools Taq PCR Master Mix, 1 μl of each primer (1 mM), and 3 μl of DNA template. The amplification consisted of an initial step of 3 min at 92 C followed by 35 cycles of 45 s at 92 C, 45 s at 52 C and 1 min at 72 C, finishing with 5 min at 72 C, and then held at 8 C. After purification of the PCR products based on paramagnetic beads technology with the CleanPCR kit (Proteigene, Saint-Marcel, France), Sanger sequencing was performed using the BigDye Terminator v3.1 Cycle Sequencing Kit (Life Technologies, Carlsbad, CA). Electrophoregrams were obtained on an ABI3500 XL apparatus (Life Technologies, Carlsbad, CA). The species was then identified using the Identification Engine of BOLD (http://www.boldsystems.org). Once a set of specimens has been identified by DNA barcode as S. delicatulus (BIN BOLD:AAE9133), specimens were re-examined to find key characteristics for distinguishing species with similar morphologies. These key characteristics were used to identify S. delicatulus among the specimens that had not been DNA barcoded.

To estimate the effect that habitat had on the life history traits, the fish age and growth rates were calculated and compared between habitats. Up to 20 individuals were subsampled from each habitat and each month based on the following criteria: (a) sizes ranging from the smallest to the largest fish in the samples; and

(b) at least five individuals for each stage unless there were fewer than five individuals for a given stage, habitat and month, when all individuals were selected. For each individual, the standard length (SL) was measured (using image processing), and the sagittal otoliths (sagittae) were extracted to estimate the age. Both otoliths were embedded in thermoplastic resin (Crystalbond 509 ® ) on the sagittal plane. The left otolith was used to estimate the age and, if it was missing or damaged, the right one was then used. Opaque daily increments (D-zone, [START_REF] Kalish | Glossary[END_REF] were counted manually from the core to the edge: two counts were done by one reader at two different times, first from the core to the edge and inversely. The maximum radius and increment radius were measured from the core to the edge. For larger otoliths that were difficult to interpret, the otoliths were polished in the sagittal plane with 2,400 grit sandpaper and then with aqueous aluminium powder (1 μm) on a polishing cloth, to see the increments more clearly.

The ages were estimated directly from the number of daily growth increments. The individual date of hatching was back-calculated by subtracting the age from the date of capture.

The otolith growth was estimated using the relationship between the otolith radius at a given age and the age. The mean increment at each age was calculated and otolith dimensions at a given age (radius and increments) were compared using ANOVA. The relationships between fish length and age were fitted by the von Bertalanffy growth model which has been used previously to describe growth of S. delicatulus (Milton et al., 1991):

SL = SL ∞ 1 -exp -Kt -t 0 ðÞ ðÞ ðÞ ð 1Þ
where SL is the standard length (mm), SL ∞ is the asymptotic length (mm), K is the growth coefficient, t is the age and t 0 is the predicted age at which SL is zero. The parameters of the growth model were estimated by non-linear least-squares fitting using the Statistica 6 ® software and the accuracy of the model was assessed using the coefficients of determination. The von Bertalanffy parameters SL ∞ and K from the least squares equations at each site were used to calculate the growth rate (dSL/dt)atSL ∞ /2.

The equation is of the form:

dSL=dt = K Ã SL ∞ =2 ð2Þ
where SL ∞ is the asymptotic length and K is the growth coefficient.

| RESULTS

The seawater temperatures in 2016 and 2017 showed two periods: February 2017 (Figure 2). At the two seagrass sites, the standard lengths were similar (7.8-37.9 mm for seagrass 1 site and 7.7-37.3 mm for seagrass 2 site), but the age ranges were different (8-108 days for seagrass 1 site and 7-65 days for seagrass 2 site).

For the other sites, the standard lengths were smaller (7.1-22.6 mm) and the maximum age was 26 days (Table 1).

| Otolith increments and hatching date

The daily growth increments were clearly visible on all 248 otoliths with radius from 27.9 to 609.2 μm and 7-108 increments. For the seagrass 1 site, there were 8-108 increments and for the seagrass 2 site there were 7-65 increments. The maximum number of daily growth increments was lower for the coral reef and harbour sites with 9-26 for the coral reef 1 site, 9-22 for the coral reef 2 site and 7-24

for the harbour site (Table 1).

Of the 248 S. delicatulus subsampled, the hatching dates were from March to October (Figure 3). There was a peak in March 2017

(n = 44). The hatching dates were irregularly distributed across the other months, with no clear peaks and none between November and February. There were differences in hatching dates between the five sites. For the seagrass sites, there was one long hatching period, from early February to late October in 2016, and again in February 2017.

For the coral reef sites, there were more than two hatching periods.

For the harbour site, there was a peak hatching period in June 2016, but with hatching in other months in lower numbers (Figure 3). There was a clear relationship between the decrease of temperatures at each site and an absence of births in the coldest period (Figure 3).

| Otolith and individual growth

Up to the tenth day, the otolith radius did not differ significantly among the five sampling sites (p > 0.05, Table 2). From 15 days old, there were significant differences among otolith radii for the different sites (p < 0.05). At 25 days old, when fish were found only in the seagrass beds, there was no difference in otolith radius. After 25 days old the otolith radius of samples were significantly different among the seagrass beds (Table 2). The otolith growth increments showed a similar pattern to the otolith radii. Up to 10 days, the otolith growth rate increased from 3.8 ± 1.3 to 8.4 ± 2.5 μm day -1 for all sites. After the tenth day, the otolith growth rates varied among sites. For the coral reef sites, the otolith growth rate increased strongly to a maximum of 14.5 ± 1.1 μm day -1 (day 18). The otolith growth rate increased from 1 to 10 days old at all sites, and then varied significantly among the five sites (Figure 4). It was highest for the coral reef sites, but the maximum age was only 26 and 22 days old (258.21 and 191.37 μm radius). For the harbour site the otolith growth rate was similar to that of coral reef sites; it was non-significantly slower. For seagrass beds, it was different between the two hatching periods. For individuals hatched during the dry season at seagrass 1, the otoliths grew more slowly than for the other sites after 12 days, and significantly slower from 31 days old (344.0 μm radius). Otoliths of fish hatched during the rainy season had similar growth among all sites (Figure 4). At seagrass 2, ages from dry season births grew strongly and were older (maximum 65 days old), while the samples hatched in rainy season had younger-age individuals (<15 days old).

The von Bertalanffy model provided a good fit to length-at-age data with a high coefficient of determination (all combined data, i.e. all sites mixed, R 2 = 0.95, Table 3). The growth model predicted that S. delicatulus grew rapidly from 7 to 30 days old (7-25 mm SL) in the five sampling sites, and that the growth was slower after 60 days old, when they remained in seagrass beds (Figure 5). For each sampling site, the von Bertalanffy model provided a less good least squared adjustment (R 2 between 0.71 and 0.91, Table 3). The estimation of the asymptotic size SL ∞ was less significant at each site (Table 3). The estimated growth coefficient (K) was different between the sampling sites: coral reef 2 showed the highest K, and the harbour the lowest K (Table 3).

| DISCUSSION

| Demography

The spatial and temporal variability in the abundance of early life history stages implies a complex set of interacting processes operating [START_REF] Doan | Plankton from Cu Lao Cham, Cu Lao Cau and Con Dao archipelago[END_REF]. The density of plankton samples collected by every light trap was very low during the north-east monsoon in Con Dao. A supposition could be that S. delicatulus larvae were carried away by these offshore currents and so did not occur at sampling sites during the north-east monsoon. [START_REF] Lecomte | Role of early life-history constraints and resource polymorphism in the segregation of sympatric populations of an estuarine fish[END_REF] reported migration of the rainbow smelt (Osmerus mordax) larvae through the water column to maximize landward transport and minimize seaward transport in the St Lawrence Estuary. Some other studies have found that clupeid larvae can also migrate through the water column [START_REF] Blaber | Diets of lagoon fishes of the Solomon Islands: Predators of tuna baitfish and trophic effects of bait fishing on the subsistence fishery[END_REF]. Although it is possible that vertical migration by S. delicatulus larvae may help them to adapt to surface currents, the hypothesis for the explanation of the pattern of captures in the Con Dao Archipelago is still untested.

Using otolith daily growth increments, the hatching dates were estimated from March to October 2016 and March to April 2017, with a very small number in February 2017, indicating that there was no spawning from November 2016 to February 2017. Milton and Blaber (1991) showed that S. delicatulus also has a protracted spawning season during the year in the tropical Indo-Pacific.

Birthdates calculated in Con Dao confirmed that the spawning period of this species is not continuous. The absence of larval hatching corresponded closely with the lowest water temperatures in this area (Figure 3), as has also been observed in Tulagi by Milton and Blaber (1991). The reproduction would therefore seem to be temperature-dependent, occurring at higher temperatures (Figure 3), which could explain the absence of fish in the capture at the end or beginning of the year. Differences in the timing of reproduction may be linked to the ocean currents and the productivity of the environment. In the Solomon Islands, S. delicatulus spawn in lagoons fringed by coral reefs where the currents are negligible (Milton & Blaber, 1991) whereas the currents in the Con Dao Archipelago are strong and seasonal [START_REF] Doan | Plankton from Cu Lao Cham, Cu Lao Cau and Con Dao archipelago[END_REF]. Most coastal marine fishes spawn buoyant eggs that drift in the surface currents [START_REF] Lobel | Transport and entrapment of fish larvae by ocean mesoscale eddies and currents in Hawaiian waters[END_REF]. Therefore, the spawning grounds chosen by fish species must ensure that larvae are recruited in the best areas [START_REF] Lobel | Reef fishes at sea: Ocean currents and the advection of larvae[END_REF]. For example, some fishes have spawning peaks that match the period when the prevailing currents are weakest, probably to avoid eggs and larvae drifting [START_REF] Johannes | Reproductive strategies of coastal marine fishes in the tropics[END_REF][START_REF] Lobel | Reef fishes at sea: Ocean currents and the advection of larvae[END_REF][START_REF] Lobel | Transport and entrapment of fish larvae by ocean mesoscale eddies and currents in Hawaiian waters[END_REF][START_REF] Watson | Ichthyoplankton of Kaneohe Bay, Hawaii: A one-year study of fish eggs and larvae[END_REF].

S. delicatulus does not reproduce in Con Dao during the north-east monsoon, and the offshore dispersion of eggs and larvae by the northward current is therefore reduced.

The highest abundance of S. delicatulus was at the harbour site in July 2016 (956 individuals captured), almost one-third of the total capture. The second highest abundance was at the seagrass 1 site in June 2016 (825 individuals) and the lowest overall abundance was at the coral reef sites. The high abundance in the harbour could be due to the characteristics of this specific habitat and town lights, which may attract some fish species [START_REF] Doherty | Light-traps: Selective but useful devices for quantifying the distributions and abundances of larval fishes[END_REF][START_REF] Leis | The larvae of indo-Pacific coral reef fishes[END_REF].

Blaxter and Holliday (1963) reported that most clupeids are attracted by artificial lights, such as Sardinops caerulea in Eastern Pacific, Clupea pallasii in the Pacific and Clupeonella spp. in the Caspian Sea. However, this does not explain the high abundance observed in the seagrass beds. Surface currents are major factors affecting the spatial distribution of the young of the year [START_REF] Harrison | Larval export from marine reserves and the recruitment benefits for fishes and fisheries[END_REF][START_REF] Robert | Larval dispersal and marine population connectivity[END_REF]. In Con Dao, as suggested earlier, the reproductive activity of the species seems to be linked to temperature and seasonal currents. These currents may also play an important role in the spatial distribution of S. delicatulus, as shown by the relationship between abundance at the sampling sites and the distance of these sites from the shore. The closest sites to the shore (harbour and seagrass 1) had FIGURE 5 Von Bertalanffy growth model for Spratelloides delicatulus (total subsample) in Con Son Bay the highest abundances, while the two coral reef sites had the lowest.

The larvae could have been carried passively by the northward currents to reach locations close to the coast (harbour and seagrass beds). However, the abundance at the coral reef 2 site was the lowest even though this site is closer to the shore than coral reef 1. The explanation could be that the coral reef 2 is in a bay of Bay Canh

Island where water currents are weaker. Hydrodynamics could explain the distribution of early stages of S. delicatulus between the various habitats [START_REF] Eckman | The role of hydrodynamics in recruitment, growth and survival of Argopecten irradians (L.) and Anomia simplex (D'orbigny) within eelgrass meadows[END_REF], but without a fine-scale map of the currents of Con Dao and a larger-scale sampling campaign, this assumption is difficult to test.

| Individual growth

For marine fishes, a change of habitat is often associated with behavioural and/or ontogenic changes or even metamorphosis and modification of the growth rates [START_REF] Linkowski | Otolith microstructure and growth patterns during the early life history of lanternfishes (family Myctophidae)[END_REF][START_REF] Ré | Growth of sprat Sprattus sprattus larvae in the German Bight (North Sea) as inferred by otolith microstructure[END_REF][START_REF] Tomás | Otolith microstructure examination and growth patterns of Vinciguerria nimbaria (Photichthyidae) in the tropical Atlantic Ocean[END_REF]. The growth rates of S. delicatulus otoliths were the same in the various habitats (seagrass beds, harbour and coral reefs) until the tenth day of life. After 10 days old there was a shift in the otolith growth between sampling sites, and the differences increased until around 26 days old. After this, the fishes were only caught in seagrass beds. For the samples hatched during the dry season, the otolith growth of samples in seagrass 1 was lower than the other seagrass after 26 days old. It underlined a probable difference in environmental factors in this habitat, inducing different growth of S. delicatulus.

The growth of S. delicatulus was rapid up to two months old and then slower in Con Son Bay, as observed in the Solomon Islands, the Maldives and Australia (Milton et al., 1991;[START_REF] Milton | Age and growth of three species of clupeids from Kiribati, tropical central south Pacific[END_REF].

S. delicatulus possibly grew slowly after two months to use energy for sexual maturity and reproduction, as the species is mature at 60-65 days old (Milton et al., 1991;[START_REF] Milton | Age and growth of three species of clupeids from Kiribati, tropical central south Pacific[END_REF]Milton & Blaber, 1991). The asymptotic size of S. delicatulus in Con Dao was much lower than that observed at the barrier reef in Townsville (Australia), while the growth coefficient was similar (Milton et al., 1991). An absence of the oldest and biggest individuals in light traps in Con Dao could explain low asymptotic size. S. delicatulus spread very early to the different habitats in Con Son Bay; the growth rates were different in each habitat, the coral reefs allowing higher growth rates than other habitats. Fish growth depends on numerous factors, such as genotype, food availability, food consumption, condition, predation pressure, competition and abiotic variables such as water temperature and salinity [START_REF] Baltz | Food, density, and microhabitat: Factors affecting growth and recruitment potential of juvenile salt marshes[END_REF][START_REF] Boeuf | How should salinity influence fish growth[END_REF][START_REF] Connell | Effects of predators on growth, mortality and abundance of a juvenile reef-fish: Evidence from manipulations of predator and prey abundance[END_REF][START_REF] Mccormick | Condition and growth of reef fish at settlement: Is it important[END_REF]. Milton et al., (1991) concluded that there was a significant negative relationship between the growth rate of S. delicatulus and water temperature at large-scale distribution. At the Townsville spot on the Great Barrier Reef, because of a wide temperature range (21-30 C) during the year, the growth was also faster (Milton et al., 1991). Temperature was identical between the different habitats in Con Dao but S. delicatulus growth was slightly different.

There were also differences even for similar habitats, for example between the two seagrass sites and between the two coral reef sites in Con Dao. One important factor that can affect the growth rates of young of the year, and that differs between habitats, is probably the food abundance [START_REF] Grol | Mangroves and seagrass beds do not enhance growth of early juveniles of a coral reef fish[END_REF][START_REF] Sponaugle | Daily otolith increments in the early stages of tropical fish[END_REF]. Spratelloides spp. feed mainly on zooplankton (Milton, Blaber, & Rawlinson, 1990). Coral reefs are extremely diverse in terms of living organisms such as zooplankton and could supply more food for early growth of S. delicatulus than other habitats, inducing higher otolith growth rates [START_REF] Grol | Mangroves and seagrass beds do not enhance growth of early juveniles of a coral reef fish[END_REF].

Previous studies have shown that the growth rate of S. delicatulus early stages was higher near a barrier reef (0.83-1.75 mm day -1 ) than in a coastal lagoon (0.63-0.74 mm day -1 ) in Solomon Islands, Maldives and Australia (Milton et al., 1991). Other factors could cause differences in the growth of S. delicatulus in various coastal habitats, but they could not be highlighted.

| Life cycle and implications for conservation

S. delicatulus found in Con Son Bay grow in two phases: first, a planktonic larval stage in seagrass, coral reef and harbour habitats, and second, after 26 days, a pelagic stage only on seagrass beds.

Larvae were distributed widely in seagrass, coral reefs and harbour habitats over the whole reproduction period. The strategy of colonizing different habitats at very young stages could be associated with the food supply and survival, which would, therefore, be more diverse, giving the best chances for the early growth and survival.

Despite the high growth rates at the coral reef sites, there was no individual older than 26 days caught at these sites. Habitat selection by fish during their life cycle is based on feeding strategy, growth rates, ontogeny, behaviour and predator avoidance [START_REF] Dahlgren | Ecological processes underlying ontogenetic habitat shifts in a coral reef fish[END_REF][START_REF] Werner | Ontogenetic habitat shifts in bluegill: The foraging rate-predation risk trade-off[END_REF][START_REF] Werner | Experimental tests of optimal habitat use in fish: The role of relative habitat profitability[END_REF]. Although the coral reefs provide a better food supply [START_REF] Grol | Mangroves and seagrass beds do not enhance growth of early juveniles of a coral reef fish[END_REF], there is a higher predation risk than in other habitats [START_REF] Chittaro | Variation in fish density, assemblage composition and relative rates of predation among mangrove, seagrass and coral reef habitats[END_REF][START_REF] Major | Predator-prey interactions in two schooling fishes, Caranx ignobilis and Stolephorus purpureus[END_REF][START_REF] Shulman | Recruitment of coral reef fishes: Effects of distribution of predators and shelter[END_REF]. In the northern Great Barrier Reef, slower-growing larvae of S. delicatulus were associated with more stress than faster growing fish because of the predation [START_REF] Villacorta | Determinants of selective mortality during the early life history of Spratelloides delicatulus in the northern great barrier reef[END_REF]. The fast growth at the larval stage can help them to speed through the high-vulnerability phase on the coral reefs [START_REF] Froese | Growth strategies of fish larvae[END_REF]. Fish can also shift between habitats to make a compromise between mortality risks and growth rates [START_REF] Dytham | Elevated mortality of fish larvae on coral reefs drives the evolution of larval movement patterns[END_REF][START_REF] Grol | Mangroves and seagrass beds do not enhance growth of early juveniles of a coral reef fish[END_REF]. Owing to the relatively short distance (less than 3 kilometres) between habitats in the sampling area (Figure 1), the early juveniles of S. delicatulus (older than 26 days) could actively migrate to seagrass beds to reduce mortality risks. Similarly, Haemulon flavolineatum (Haemulidae) juveniles were found at higher densities in seagrass beds, despite higher growth rates on coral reefs [START_REF] Grol | Mangroves and seagrass beds do not enhance growth of early juveniles of a coral reef fish[END_REF]. In addition to movement strategies of fish larvae in coral reef sites, there were probably also high mortality rates of S. delicatulus at these sites for this species with a short life cycle. There could have been a high predation pressure that occurred at coral reef sites during the sampling period, which resulted in a high mortality rate of S. delicatulus larvae. In the Solomon Islands, Spratelloides spp. are also recorded as important prey in coral reef fish communities [START_REF] Blaber | Diets of lagoon fishes of the Solomon Islands: Predators of tuna baitfish and trophic effects of bait fishing on the subsistence fishery[END_REF]. The present results on early life history of S. delicatulus in Con Dao demonstrate that seagrass beds are nursery areas for S. delicatulus after the larval stage.

Coral reef fishes are very diverse and are the basis of a major fishery in the Con Dao Archipelago [START_REF] Nguyen | Coral reef fishes in the Con Dao Archipelago[END_REF]. Thus, protection and conservation of S. delicatulus, a low-trophic-level species, is very important for respecting the trophic network and fishery management, and for ichthyophageous species living in the same environments. Improving its conservation will maintain sustainable ecological processes, and resources to ensure the continued fishing of high-value targeted predator species such as Lutjanus vitta, Auxis thazard, Megalaspis cordyla and Scomberoides lysan.

Connectivity, linking local S. delicatulus populations through the dispersal of larval and juvenile stages has important implications for habitat conservation, the persistence of metapopulations and resilience from environmental pressures [START_REF] Almany | Connectivity, biodiversity conservation, and the design of marine reserve networks for coral reefs[END_REF][START_REF] Sale | Critical science gaps impede use of no-take fishery reserves[END_REF].

The present study has shown that different coastal habitats (seagrass, coral reef, harbour) play different roles in the life cycle of this key pelagic fish species in the Con Dao MPA. Seagrass beds are the key habitats for juvenile growth of S. delicatulus in this MPA. Currently, there is only a very small area of seagrass bed that is protected in this MPA, which is based on separate patches of protected zones (Figure 1). For example, in Agatti island (India), S. delicatulus populations declined because the seagrass beds were reduced [START_REF] Arthur | Shared spaces: First and second-order conflict in the use of seagrass habitats by greenturtles and fisher communities in the Agatti lagoon[END_REF]. Thus, more protection of seagrass beds in Con Dao is needed to conserve S. delicatulus and, probably, similar species. In addition, owing to the current fragmentation of the Con Dao MPA, many coral reefs are not protected in the Con Son Bay (Figure 1), whereas coral reefs are also key habitats for early stages of S. delicatulus. Establishing a network of continuous areas linking habitats, without patches, could improve the conservation of S. delicatulus not only in Con Dao, but also elsewhere in the tropical Indo-Pacific.

  a slightly lower seawater temperature from November 2016 to February 2017 (north-east monsoon), (25-28 C), and a higher seawater temperature from June to October 2016 (south-west monsoon) and March to April 2017 (29-31 C). The mean temperatures did not vary much among the five sampling sites across the months (28.7 C ± 0.06). The salinity was similar among the five sample sites (32.7 ± 0.5). A total of 160 individuals were identified genetically as S. delicatulus (BIN BOLD:AAE9133) in order to then recognize a total of 3,581 individuals of S. delicatulus morphologically among the total sample. The highest number of S. delicatulus was collected at the harbour site in July 2016 (956 specimens), and the second highest was collected at seagrass 1 site in June 2016 (825 specimens). No specimens were found in January 2017 and

  across various scales to produce the observed patterns: density and reproductive period, physical dispersal processes, migratory behaviour (e.g. vertical migration), predator/prey mediated survival, available habitats for settlement, post-settlement survival and larval condition[START_REF] Robert | Larval dispersal and marine population connectivity[END_REF]. During the one-year sampling, this species was found continuously from June to December 2016 and then from March to April 2017 (end of the sampling), but fish were not observed in January and February 2017. This absence could be explained by an active avoidance of the light traps or non-attraction to the light. There are two main currents in Con Son Bay during the year: the northward current from offshore to the inshore during the south-west monsoon (April to October) and the reverse current during

FIGURE 2

 2 FIGURE 2 Spratelloides delicatulus caught each month by light-traps between June 2016 and May 2017 at the five sites in Con Son Bay (total number of fish caught = 3,581)

FIGURE 4

 4 FIGURE 4 Mean otolith radius of Spratelloides delicatulus from 1 to 45 days old for the five sites, distributed during the two hatching periods (dry season from February to July, and rainy season from August to November) at Con Son Bay

TABLE 1

 1 Size and age of Spratelloides delicatulus young of year for the five sites of the Con Son Bay

			Standard length (mm)		Age (days)
	Site	n	Mean ± SD	Range	Mean ± SD	Range
	Seagrass 1	92	20.4 a ± 8.6	7.8-37.9	39.4 a ± 29.0	8-108
	Seagrass 2	28	16.2 b ± 9.4	7.7-37.3	21.4 b ± 17.5	7-65
	Coral reef 1	40	14.5 bc ± 3.3	7.1-22.6	17.7 b ± 4.4	9-26
	Coral reef 2	18	13.7 bc ± 3.4	7.6-18.8	15.0 b ± 4.5	9-22
	Harbour	70	12.0 C ± 2.0	7.5-16.8	14.2 b ± 4.1	7-24

Means with different letters in superscript are significantly different (one-way ANOVA, P < 0.05).

FIGURE 3 Temporal distribution of Spratelloides delicatulus hatching dates back-calculated from otolith readings (histograms) and mean of sea surface water temperature (points and line) for the five sites in Con Son Bay

TABLE 2

 2 Spratelloides delicatulus otolith radius and growth increment as a function of age for the five sites in Con Son Bay

		Mean otolith radius (μm)				Mean growth increment (μm)
	Age (day)	G1	G2	R1	R2	H	P 1	G1	G2	R1	R2	H	P 2
	5	22.7 a	22.6 a	22.1 a	21.5 a	20.2 a	0.09	5.3 a	5.6 a	5.6 a	5.5 a	5.0 a	0.48
	10	57.5 a	67.1 a	60.8 a	61.2 a	56.7 a	0.13	7.7 a	9.5 b	8.9 ab	8.9 ab	8.3 ab	0.00
	15	93.6 a	117.1 b	107.7 b	115.6 b	99.8 ab	0.00	7.6 a	9.4 b	10.7 b	11.5 b	9.6 b	0.00
	20	124.7 a	162.9 b	169.6 b	174.7 b	151.2 ab	0.01	7.54 a	9.89 ab	12.15 b	13.17 b	10.47 b	0.00
	25	164.0 a	196.4 a	--	-	0.12	8.3 a	9.0 a	---	0.57
	30	203.5 a	247.1 a	--	-	0.11	8.4 a	9.8 a	---	0.33
	35	220.6 a	298.8 b	--	-	0.00	7.7 a	10.1 b	---	0.04
	40	229.5 a	349.4 b	--	-	0.00	6.4 a	9.5 b	---	0.00
	45	251.7 a	397.0 b	--	-	0.00	6.6 a	9.7 b	---	0.00
	50	285.3 a	439.3 b	--	-	0.00	6.6 a	10.4 b	---	0.00
	55	318.5 a	491.6 b	--	-	0.00	6.7 a	10.7 b	---	0.00

G1, Seagrass 1 site; G2, seagrass 2 site; R1, coral reef 1 site; R2, coral reef 2 site; H, harbour site; P 1 , P-value of ANOVA test for otolith radius between habitats; P 2 , P-value of ANOVA test for otolith growth increment between habitats. Means with different letters in superscript are significantly different (one-way ANOVA, P < 0.05).

TABLE 3

 3 Parameter estimates and coefficient of determination R 2 for the von Bertalanffy model of Spratelloides delicatulus from five sites in Con Son Bay

	Sites	SL ∞ (mm)	P-value	K (year -1 )	P-value	Growth rate (mm year -1 )	R 2
	Seagrass 1	58.8	0.71	3.4	0.78	101	0.81
	Seagrass 2	2085.3	0.99	0.2	0.99	156	0.87
	Coral reef 1	107.4	0.89	2.3	0.91	123	0.79
	Coral reef 2	22.9	0.01	28.9	0.31	332	0.91
	Harbour	522.1	0.99	0.3	0.99	65	0.71
	All sites	38.3	0.00	8.1	0.00	155	0.95

the north-east monsoon (November to March)

(Doan &

ACKNOWLEDGEMENTS

The authors wish to thank students at the Laboratory of Zoology, University of Science (VNUHCM), and local people in the Con Dao Archipelago, who helped in the field and laboratory experiments. The Con Dao National Park supported this study to be conducted in the marine protected areas. Genetic barcoding was carried out by the GenSeq facility at the 'Institut des Sciences de l'Evolution de Montpellier'-LabEx 'Centre Méditerranéen de l'Environnement et de la Biodiversité' . We are indebted to Eric Desmarais, Frédérique Cerqueira and Thomas Cantinelli (UMR ISEM, Montpellier, France) for their important contribution to the barcoding realised through the GenSeq technical facilities of the 'Institut des Sciences de l'Evolution de Montpellier'-LabEx 'Centre Mediterraneen de l'Environnement et de la Biodiversite'. We are grateful to David McKenzie (UMR MARBEC, Montpellier, France) for English editing. http://fondation. total.com

Funding information

Fondation Total, Grant/Award Number: DECODIV; IRD doctoral grant, Grant/Award Number: ARTS

CONFLICT OF INTERESTS

The authors declare that they have no conflicts of interest regarding the publication of this article.

FUNDING INFORMATION

Fondation Total (http://fondation.total.com): DECODIV Project; IRD doctoral grant funding (ARTS); the MARBEC Mixed Research Unit and the SEDES International Joint Laboratory (IRD).


P Pilleri

Z Chen

A Cousin

S Maurice

O Forni

R Xin

Chunlai Li

R Shu

O Gasnault

R C Wiens

Comparison of ChemCam, SuperCam and MarSCoDe LIBS instruments on Mars

Introduction: Laser-induced breakdown spectroscopy (LIBS) has become a recognized technique for in-situ geochemical analysis in planetology over the last decade [START_REF] Wiens | Laser Induced Brakedown Spectroscopy[END_REF]. Following the legacy of the Chem-Cam instrument [START_REF] Wiens | [END_REF]3] onboard the Curiosity rover, which landed in Gale crater on Mars in 2012, two additional instruments are using this technique for Mars exploration: SuperCam onboard Perseverance [4,5], which landed in the Jezero crater in 2021, and MarSCoDe onboard Zhurong [6], which landed in 2021 in Utopia Planitia and is the first Chinese mission on Mars.

The basic principle of the LIBS analysis in these instruments is to focus an infrared laser on a target within ~7 m of the rover thus creating a plasma of ablated material. The light from the plasma is then captured by the telescope and transferred to the spectrometers for registration. Thus, all these LIBS shots translate into a spectrum in the ultraviolet (UV) violet (VIO) and near infrared (NIR) domains. ChemCam was the first to investigate the surface of Mars with this technique and has now analyzed more than 3500 rock and soil targets. Each target is sampled at several positions, constituting a "raster", in order to observe spatial inhomogeneities. Each point of a "raster" is actually shot several times (usually 30) in order to improve the statistical significance of the collect, improve the signal to noise ratio (SNR), and differentiate surface properties (dust) and the interior of the target. The LIBS analysis is accompanied by a highresolution remote-micro-imager observation [7], to provide context of the target that has been sampled.

The collected spectra are cleaned and calibrated by an ad-hoc pipeline. Quantification models are then applied to the spectra [8,9,[START_REF]pdf 54th Lunar and Planetary Science Conference[END_REF] by comparing the spectral signatures observed on Mars with a laboratory database obtained with a copy of the instrument. ChemCam has 10 calibration targets onboard the rover [7,8], with the purpose of validating the performance of the instrument along the mission, and to verify that the quantitative models give consistent results on targets of very well-known compositions.

Thanks to the lessons learned from ChemCam, SuperCam contains more LIBS calibration targets (23 in total), with the goal of validating the models on a wider range of compositions. A replica of the Sher-gottite calibration target on ChemCam was included on SuperCam with the goal of allowing a crosscomparison of the two instruments, and allow a comparison between the results in Gale and Jezero. For a similar goal, the MarSCoDe instrument onboard Zhurong, has 12 calibration targets and one of them is a Norite, a replica from ChemCam. The three instruments also each have a titanium target that is used mainly for wavelength calibration.

To summarize, there are now three rovers at the surface of Mars using the same LIBS technique, and their data can be compared via a reference target to ChemCam. Also, the LIBS technique being sensitive to matrix effects, each instrument has developed a laboratory database for quantitative purposes, which contains several common samples. A cross-calibration can therefore be very interesting to make the databases usable for the three different instruments. The goal of this study is to give the context of each instrument, describe their specificities (spectral range, resolution, SNR, irradiance), and compare the spectra obtained from their common calibration targets.

Results: The spectral comparison is made using the calibration targets that the three instruments have in common (Norite and Shergottite, as well as Titanium). The data processing for the spectra coming from all the instruments is very similar, and thus the comparisons have been made using the cleaned and processed spectra available on the planetary data system (PDS). Lines have been fitted using a Voigt function in order to check the signal-to-noise ratio, resolution of each spectrometer and line intensity ratios. Spectral performance. The three instruments cover the UV, VIO and Near-IR spectral ranges. They all start at ~240 nm and extend to the near-IR up to ~850 nm (SuperCam, MarSCoDe) or 906nm (ChemCam). However, ChemCam and SuperCam have a gap between ~341 and 382 nm, while MarSCoDe spectral coverage is continuous. The spectral resolution is similar for the three instruments, with each instrument performing better in a given wavelength range. Because MarSCoDe's operating range extends farther down, to -60 Deg C, thermal effects on the detectors can impact the wavelength stability. This will need to be assessed and corrected using the Ti spectra, as done for ChemCam. Signal To Noise Ratio. We calculated the signal to noise ratio by performing a line fitting at different wavelengths, and comparing with the standard deviation in a close-by region with no spectral lines. The SNR is very similar for the three instruments in the UV and VIO range, but ChemCam and SuperCam have better performances in the VIO range. These can be due to a number of effects, such as a different spot size, which is smaller for MarSCoDe (See table 1), the higher irradiance for SuperCam, and different focus accuracies. MarSCoDe has a variation of spot size and optical alignments as a function of the operating temperature [6], especially in the range below -20 Deg C.

Shot-to-shot stability.: In order to evaluate the shot-to-shot stability in the different instruments, we calculate the standard deviation over the mean of the total signal collected in the different spectra acquired on a given calibration target. For Norite and Shergottite, each LIBS activity consists of 30 shots (thus 30 spectra), whereas only 10 shots were performed on the Titanium target. ChemCam spectra proved to be very stable, especially in the UV and in the nearinfrared. Stability is very similar in the VIO for ChemCam and SuperCam. However when using Shergottite and Norite, obtained with 30 shots, the three instruments are overall similar.

Line peak ratios. We have compared the spectra of Norite targets from ChemCam (Sol 27) and MarSCoDe (Sol 41). The presence of atomic emission was visually similar while certain inconsistencies in line ratios could be observed. The line intensities of 9 elements (Al, Si, Ti, Fe, Ca, Mg, Na, K, O) were compared (after normalization to the Ca-393.5 nm line). The normalized intensities follow the 1:1 line well with good R-squares. The ratios of normalized intensity shows no significant dependency on the wavelength so it may not be largely attributed to the general difference in instrumental responses. It is thus assumed that the difference in relative intensities was mostly induced by the difference in excitation, given the nearly identical norite materials.

Conclusions

With three rovers at the surface of Mars that are each equipped with a LIBS instrument, understanding their differences in design and perfor-mance is important for a consistent comparison of their results. A complete cross-calibration of the three instruments and of the spectral database used for quantification, is needed to compare results on elemental compositions. In the long term this will allow to compare variations in the elemental composition of dust, rocks and soils in three different sites on Mars.

  Planetary Science Conference 2023 (LPI Contrib. No. 2806)

Acknowledgments:

The engineers and scientists of the Perseverance, Curiosity and ZhuRong rovers are thanked for their generous contributions to this work. This work was supported by CNES in France and by the Mars Exploration Program in the US.


Alexandre Letard

Tassadit Amghar

Olivier Camp

Nicolas Gutowski

COM-MABs: From Users' Feedback to Recommendation

Introduction

Multi-Armed Bandit (MAB) approaches [START_REF] Robbins | Some aspects of the sequential design of experiments[END_REF] have been extensively applied in various fields of activities as finance, healthcare or recommendation systems (Bouneffouf and Rish 2019). Through an iterative process, MAB algorithms are designed, at each round, to choose from a set of actions the one that maximizes their expected gain. They obtain good performances from a global accuracy metric view point. However, in many applications, like recommender systems [START_REF] Chen | Combinatorial multiarmed bandit: General framework and applications[END_REF], several answers may be correct and thus, more than one item should be selected at each round. COMbinatorial Multi-Armed Bandits (COM-MAB) [START_REF] Anantharam | Asymptotically efficient allocation rules for the multiarmed bandit problem with multiple plays-part i: I.i.d. rewards[END_REF] have been specifically designed to allow the selection of multiple arms and are thus well suited. Both MAB and COM-MAB approaches are reinforcement learning approaches in which an agent performs an action, observes a reward and changes its state [START_REF] Sutton | Reinforcement learning: An introduction[END_REF]. For recommender systems, the performed action is a recommendation and the reward is computed from the corresponding user feedback from which the MAB agent learns [START_REF] Gutowski | Context-aware recommendation systems for cultural events recommendation in Smart Cities[END_REF]. Hence, several feedback strategies have been implemented for the COM-MAB approaches [START_REF] Audibert | Minimax policies for combinatorial prediction games[END_REF]. Those strategies can be used with either the user's feedback for every arm composing the recommendation -herein, referred to as full feedback vector setup (FV) - [START_REF] Combes | Combinatorial bandits revisited[END_REF], a part of them -herein, referred to as partial feedback vector setup (P) - [START_REF] Saha | Combinatorial bandits with relative feedback[END_REF] or with implicitly deduced feedback values from sparse vectors [START_REF] Kveton | Combinatorial cascading bandits[END_REF]. From an industrial view point, those topics are particularly relevant and impactful for applications in direct interactions with users aiming at performing top-k recommendation with restricted feedback ψ ≤ k.

Without records of prior interactions between the recommender system and the users, a fitting feedback strategy becomes essential for the efficient learning of a COM-MAB algorithm. However, most previous works either employ the Bandit [START_REF] Ito | Improved regret bounds for bandit combinatorial optimization[END_REF], Semi-Bandit [START_REF] Combes | Combinatorial bandits revisited[END_REF] strategies, or partial variants considering the feedback given for the ψ arms with highest reward expectations from the initial recommendation [START_REF] Saha | Combinatorial bandits with relative feedback[END_REF]. Further investigation is needed to observe how those strategies can improve the performances of COM-MAB approaches.

Thus, inspired by Letard et al., we formally model a feedback strategy as the succession of three processes : a) "Feedback Identification"; b) "Feedback Retrieval"; and c) "Reward Computing". We argue that, there is no unique optimal feedback strategy and thus that, depending on the application settings and the chosen COM-MAB algorithm, those underlying processes can be worked on and combined to improve the performances of the learning agent. To confirm this assumption, we propose a new Reward Computing process, "Bandit Under Semi-Bandit Conditions" (BUSBC). Our approach is built-upon the combination of methods from the literature and aims at enhancing the accuracy of Upper Confidence Bounds (UCB) based COM-MAB algorithms. The impact of each process composing a feedback strategy on the global accuracy metric was evaluated under both full feedback vector and partial feedback vector setups. Our results confirm our hypothesis as BUSBC Reward Computing process significantly increases the performances of UCB-like algorithms. Depending on the application and method from the literature, the observed improvement range from 0.5% to 16.2%, with an average of 4.7%.

The paper is organized as follows. In section 2 we review works related to the COM-MAB problem and feedback strategies. Section 3 depicts our general model for a feedback strategy and our proposed method, BUSBC. Section 4 discusses our experimental evaluation. Finally, we conclude and open up new perspectives in Section 5.

Preliminaries

Combinatorial Multi-Armed Bandits

A MAB problem [START_REF] Robbins | Some aspects of the sequential design of experiments[END_REF]) includes a set A = {a 1 , ..., a m } of m independent arms, where each arm a ∈ A is an item to recommend. As part of a recommendation system, at each iteration t ∈ [1, T ], with T being a known horizon, a learning agent selects an arm a t ∈ A according to its policy π and recommends it to the user. Herein, we consider the COM-MAB problem [START_REF] Anantharam | Asymptotically efficient allocation rules for the multiarmed bandit problem with multiple plays-part i: I.i.d. rewards[END_REF] which is a generalization of the MAB problem employed to recommend sets of arms

A k = {a 1 , ..., a k }, A k ⊆ A, with 1 ≤ k ≤ m, ∀t ∈ [1, T ].
Among the existing COM-MAB approaches, we consider the "Multiple Plays" method [START_REF] Anantharam | Asymptotically efficient allocation rules for the multiarmed bandit problem with multiple plays-part i: I.i.d. rewards[END_REF] which allows the sequential use of classical MAB algorithms in order to iteratively construct a "Super-Arm" as follows: while

|S t | < k, S t = ∪ k i=1 {a i }, where a i = argmax π a∈A\St E[R t,a ]
. Super-Arm S t is thus the subset of k arms having the highest reward expectations according to the MAB algorithm's policy π. Hence, any single play algorithm of the literature can be used in a combinatorial setting.

In a stochastic setting, where the rewards are i.i.d random variables, a COM-MAB algorithm of policy π aims at minimizing the cumulative regret ρ π (T ) = T µ * -T t=1 r t , where µ * is the reward expectation of the optimal superarm, without prior knowledge of the rewards probabilities distribution µ a ∈ [0, 1] over each arm a of A. Many realworld applications prefer to consider the maximization of the global accuracy metric Acc π (T ) = T t=1 rt T . Traditionally, MAB algorithms update their policy by a summation of the observed rewards R t for each arms : SR t,a = SR t-1,a + R t,a . With R t being either a scalar value or a vector R t = {R t,1 , R t,2 , ..., R t,ψ }, with ψ being the number of arms for which feedback has been provided at iteration t. As works on feedback strategies impact those observed rewards, we consider r t = 1 if at least half of the suggested items in S t satisfy the user, and r t = 0 otherwise (See Subsection 4.1) as assessment variable for a fairer evaluation of the studied methods on the global accuracy metric.

Feedback Strategies

COM-MAB algorithms' learning is mainly led by the rewards observed at each round. Hence, the reward function of such algorithm is of utmost importance. Feedback strategies are reward functions specifically designed for agents in interaction with humans, such as in recommender systems. Several strategies have thus been implemented to consider the feedback at each iteration t in order to compute the reward R t observed by a COM-MAB algorithm (Audibert, Bubeck, and Lugosi 2011). Hence, we denote Y t = {Y t,1 , Y t,2 , ..., Y t,m }, the feedback vector associating a specific feedback to each arm a of A at round t. One should notice that Y t denotes an abstract concept, since feedback can not be acquired for not recommended arms in real-world applications. More realistically, Y t can represents the user's possibilities of feedback while we denote the actual feedback given by user u t as F t , with F t ⊆ Y t .

To the best of our knowledge, most traditional approaches are variants of the four following models: a) Full-Information [START_REF] Audibert | Minimax policies for combinatorial prediction games[END_REF], where an individual reward is observed for every arm a of A, whether they were in S t or not: R F I t = F t = Y t ; b) Semi-Bandit [START_REF] Combes | Combinatorial bandits revisited[END_REF], where the individual reward of each arm a of S t are revealed: R SB [START_REF] Ito | Improved regret bounds for bandit combinatorial optimization[END_REF], where only a cumulative reward1 associated to S t is observed by the agent: R B t = S ⊤ t R SB t ; d) Cascading Bandits models [START_REF] Li | Contextual combinatorial cascading bandits[END_REF], where the reward function is dependent of the application, and aims at deducing implicitly F t , considering a stopping criterion. One may know, from the literature [START_REF] Neu | First-order regret bounds for combinatorial semibandits[END_REF], that Semi-Bandit and Bandit depict both an application setting, modelling constraints on user feedback acquisition, and a method for computing the rewards from the provided user feedback. Herein, for clarity's sake, we only refer to them as rewards computing processes and express the feedback acquisition constraints by full or partial feedback vector setups.

t = F t = {Y t,a | a ∈ S t } ; c) Bandit
Audibert, Bubeck, and Lugosi have proven that, among those approaches, the Semi-Bandit method is often the most efficient. This approach has thus been extensively studied in the literature [START_REF] Sankararaman | Semi-bandit feedback : A survey of results[END_REF]. However, for some real-world applications S t can be large [START_REF] Lagrée | Multiple-play bandits in the position-based model[END_REF]. To prevent the user from having to return an equally large feedback vector, partial variants have been proposed [START_REF] Luedtke | Asymptotically optimal algorithms for multiple play bandits with partial feedback[END_REF]. When partial feedback strategies are used, the observed feedback vector is only defined for a subset P t ⊆ S t . More formally, for non-partial approaches, the size of the observed feedback vector is |F t | = |S t |, while with partial methods |F t | = ψ with ψ < |S t |. Hence P t is a request vector for feedback while F t is its corresponding answer provided by user u t , both with same dimension ψ. Herein, in both cases, the goal of the agent is to perform top-k recommendation, while learning with ψ ≤ k user feedbacks at each iteration.

System Model

Feedback Strategy: A General Model

Let U = {u 1 , ..., u n } be a set of n users. At each iteration t ∈ [1, T ], a user u t is pending for a recommendation S t of k items from A = {a 1 , ..., a m }, where A is the set of items known by a recommender system built-upon a COM-MAB algorithm of policy π. We argue that all the previously introduced feedback strategies, used by COM-MAB algorithms, conform to the following three-process general model:

Feedback Identification: where a set of arms P t ⊆ A, for which feedback will be requested to the user, is determined. with Cascading Bandits models, this step is used to define a stopping criterion while the user interacts with the system, e.g., the selection of a preferred item associated with arm a s . Under a partial-vector setup, this step defines how to construct P t from S t . Other approaches consider either P t = A or P t = S t . This process can be considered as problem dependant, to some extent. Indeed, the number ψ of obtained feedbacks at each iteration, is either specific to an application or restricted by user's fatigue. However, the choice of which arms for which feedback will be provided is problem free and can be decided by the recommender system. Besides, Active Learning [START_REF] Elahi | A survey of active learning in collaborative filtering recommender systems[END_REF], an emerging research area, focus on dealing with user's feedback scarcity leading to the cold-start problem. The objective is to identify the items for which feedback will be most useful to better estimate the arms' reward expectation. In most works, sub-optimal arms are thus recommended to users for a sign-up period. However, Feedback Identification process can be used to perform active learning among the determined optimal arms, leading to an improvement over feedback usefulness without sacrificing accuracy.

Feedback Retrieval: where an initial feedback vector F t is built. Except for cascading bandits models, the other methods presented in sub-section 2.2 require an explicit feedback from the user. In Cascading Bandits based feedback strategies, this step is used to infer F t by considering the relative distances of each arm a in S t from the arm a s triggering the defined stopping criterion. These methods, particularly used in applications where a great number of items are recommended simultaneously to users, allow a more flexible behavior from the recommender system and reduce users' fatigue. Hence, many works have shown the interest of the Feedback Retrieval process with Cascading Bandits variants [START_REF] Li | Contextual combinatorial cascading bandits[END_REF][START_REF] Kveton | Combinatorial cascading bandits[END_REF].

Reward Computing: where the final reward R t , observed by the agent, is computed from F t . Thus, R t can either be the feedback vector F t or the result of any processing on F t , i.e., the inner product between F t and P t . This process is usually not problem-dependant : as we show in our experiments (see section 4.2), the fittest method for this step is mostly dependant of the chosen COM-MAB algorithm. As even minute changes can lead to significant differences on performances, we consider this step as an easy and consistent way to improve recommender systems.

Bandit under Semi-Bandit Conditions: BUSBC

Following the previously exposed general model (section 3.1), we implemented a novel Reward Computing process, BUSBC. This method aims at enhancing the performances of UCB-based COM-MAB algorithms.

As in any feedback strategy, Feedback Identification and Feedback Retrieval are performed before the reward computing. Herein, we consider that Feedback Retrieval is processed by explicitly requesting feedback from user u t . Under the full feedback vector setup, ∀a i ∈ S t , a feedback is requested from the user, i.e., P t = S t . Under the partial feedback vector setup, feedback will only be given for ψ < k arms. The feedback vector is thus only defined for a subset P t ⊆ S t where P t is constructed incrementally such that: P t = P t,ψ with P t,0 = ∅ and ∀j ∈ [1, ψ]; P t,j = P t,j-1 ∪ {a i } where a i ∈ S t is selected according to the chosen Feedback Identification process (lines 1 to 4 of algorithm 1). In this article, we consider and further explore the following methods proposed by Letard et al.: Reinforce -RE: which depicts the most popular Feedback Identification process in the literature, and consists in a scale reduction of the full feedback vector setup. It selects the ψ arms from S t with the highest reward expectations E[R t,a ]:

a i = argmax π a∈St\Pt,j-1 E[R t,a ] (1)
Optimal-Exploration -OE: This approach aims at maximizing the agent's knowledge on the reward expectation distribution {µ 1 , ..., µ k }. It selects the ψ arms from S t for which the least feedbacks have been provided till t:

a i = argmin a∈St\Pt,j-1 obs a,t (2)
where obs a,t is the number of observed feedbacks for arm a up to iteration t.

In the Feedback Retrieval process, we construct the feedback vector F t from Y t by requesting feedback from user u t for each arm a in P t (line 5 of algorithm 1):

F t = {Y t,a | a ∈ P t } (3)
As the Reward Computing process, BUSBC firstly calculates a cumulative reward R B t from this feedback on the current recommendation (line 6 of algorithm 1), such that :

R B t = P ⊤ t F t (4)
Then the COM-MAB algortihm observes this reward and updates its policy only for the arms in P t for which a positive feedback has been provided (lines 7 to 11 of algorithm 1) :

∀a ∈ P t , if F t,a > 0 : SR t,a = SR t-1,a + R B t (5)
where SR t,a is the sum of observed rewards for arm a until iteration t.

Algorithm 1 depicts the BUSBC approach when used under a partial feedback vector setup with OE as the Feedback Identification process. To change the identification process to RE, line 3 should be replaced by the corresponding selection mechanism defined by equation 1. Similarly, to consider the full-vector application of BUSBC, lines 2 to 4 should be removed and replaced by P t = S t . The Bandit approach can be inefficient in some cases. This can be explained both by unrealistically high rewards and by rewards provided to unsatisfying arms in S t . The second issue can be addressed by only providing successful arms in S t with the cumulative reward as in a Semi-Bandit strategy with Bernoulli rewards. Concerning the first issue, we believe that for optimistic COM-MAB approaches, a cumulative reward may, in actual fact, be an advantage. Thus, BUSBC is mainly designed to enhance UCB-based COM-MAB algorithms. 1). For each dataset and for each arm, we consider user feedback as Bernoulli variables i.e., for each arm, F t,a = 1 if the user considers the recommended item (arm) as relevant or 0 otherwise. For Jester and MovieLens datasets, where feedbacks are a rating between 0 and 5, arms are considered relevant if their rating is greater than or equal to 4. Algorithms & Baselines: Our goal is to observe the impact of the studied feedback strategies on the performances of a COM-MAB algorithm, with regards to its policy π. Thus, in our experiments, we applied the multiple plays method [START_REF] Anantharam | Asymptotically efficient allocation rules for the multiarmed bandit problem with multiple plays-part i: I.i.d. rewards[END_REF] to the following popular MAB approaches :

• ε-greedy [START_REF] Sutton | Reinforcement learning: An introduction[END_REF], with ε = 0.0009 • Thompson Sampling (TS) [START_REF] Agrawal | Analysis of thompson sampling for the multi-armed bandit problem[END_REF] • Upper Confidence Bounds (UCB) 1 & 2 [START_REF] Auer | Using confidence bounds for exploitationexploration trade-offs[END_REF] We chose those algorithms because they are the background methods of a number of state of the art algorithms and do not take advantage of any problem dependant optimisation. Therefore, we believe that the improvements observed on those algorithms would also be observed on their more specific derived methods. Nevertheless, in this work, the COM-MAB algorithms are mainly the required support to allow an evaluation of feedback strategies. We compare our proposed BUSBC Rewards Computing process with the following baselines, still used in the literature:

• Bandit (B) [START_REF] Ito | Improved regret bounds for bandit combinatorial optimization[END_REF] • Semi-Bandit (SB) [START_REF] Combes | Combinatorial bandits revisited[END_REF] • Bandit and Semi-Bandit (BSB) [START_REF] Letard | Partial bandit and semi-bandit: Making the most out of scarce users' feedback[END_REF] Evaluation Metric: We consider the global accuracy (Acc) metric [START_REF] Gutowski | Context-aware recommendation systems for cultural events recommendation in Smart Cities[END_REF] as defined by the following equation:

Acc(T ) = T t=1 r t T (6)
As explained in sub-section 2.1, r t ∈ {0, 1}, is an unknown evaluation reward modeling user u t 's overall opinion of recommendation S t . Its only purpose is to be used in the computation of the global accuracy and thus remains unknown to the agent. The reward r t is computed using the feedback provided for each arm a of S t as follows:

r t = 1 if k a=0 Y t,a ≥ k 2 , with Y t,a ∈ {0, 1} 0 otherwise (7)
The rewards observed by a COM-MAB algorithm (R t ) are built following the considered feedback strategy and based on the acquired feedback. Therefore, such an independent assessment variable (r t ) is essential for a fair evaluation of the competitive approaches.

Experimental Protocol: We compare each Reward Computing process by experimenting them for each algorithm and dataset, under both the full-vector and partial-vector setups. In the partial-vector setup, we consider Optimal-Exploration (OE) and Reinforce (RE) as Feedback Identification processes. For each experiment, we simulate 10 cyclical iterations with a finite horizon of T = 10 000 rounds. The studied feedback strategies are identified by their parameters and named S-C-I, with : S: Feedback Setup (FV or P). C: Reward Computing process (B, SB, BSB or BUSBC). I: Feedback Identification process (OE, RE or "/" if FV).

Real-world applications are rarely equiprobabilistic, which can lead to biased performances when evaluating models. For example, only a third of the feedbacks stored in RSASM are positive. In other words, on this dataset, each user consider on average 6 arms as relevant. 2 Hence for each dataset, a more in-depth study of optimal values for k, the number of items to recommend at each iteration, should be done. However, as our purpose is to observe feedback strategies' impact on COM-MAB algorithms' global accuracy, we avoid those biaises by performing experiments with k = 6 for every chosen dataset (RSASM being the worst case scenario). Concerning the ψ number of feedback observed at each iteration, this study focus on worst case scenario to ensure benefits for any real-world application. Saha and Gopalan have shown that, under partial feedback setup, ψ = 2 gave worst performances, which is thus the chosen value for our experiments. In Tables 2 and3 we observe each algorithm's global accuracy when applied with a specific feedback strategy. Finally, in subsection 4.2 we analyse our results. We performed Kruskal-Wallis and Wilcoxon signed rank tests over the global accuracy to ensure the observed differences are significant.

Results Analysis

RSASM Jester MovieLens Algorithm Strategy Acc(T ) Acc(T ) Acc(T ) ε-greedy
FV-B-/ 0,490 ±0, 044 0,402 ±0, 003 0,879 ±0, 006 FV-BSB-/ 0,551 ±0, 008 0,416 ±0, 007 0,907 ±0, 007 FV-BUSBC-/ 0,557 ±0, 008 0,436 ±0, 005 0,919 ±0, 004

FV-SB-/ 0,555 ±0, 008 0,453 ±0, 006 0,928 ±0, 003 TS FV-B-/ 0,351 ±0, 071 0,193 ±0, 017 0,853 ±0, 005 FV-BSB-/ 0,390 ±0, 051 0,395 ±0, 018 0,855 ±0, 005 FV-BUSBC-/ 0,528 ±0, 027 0,415 ±0, 009 0,883 ±0, 010

FV-SB-/ 0,564 ±0, 004 0,446 ±0, 005 0,923 ±0, 003 UCB FV-B-/ 0,488 ±0, 004 0,402 ±0, 004 0,853 ±0, 004 FV-BSB-/ 0,557 ±0, 005 0,407 ±0, 004 0,873 ±0, 004 FV-BUSBC-/ 0,563 ±0, 004 0,431 ±0, 005 0,921 ±0, 004

FV-SB-/ 0,555 ±0, 004 0,404 ±0, 006 0,759 ±0, 004

UCB2

FV-B-/ 0,488 ±0, 004 0,173 ±0, 005 0,871 ±0, 012 FV-BSB-/ 0,545 ±0, 011 0,177 ±0, 004 0,874 ±0, 005 FV-BUSBC-/ 0,559 ±0, 005 0,183 ±0, 003 0,915 ±0, 005

FV-SB-/ 0,545 ±0, 005 0,178 ±0, 002 0,837 ±0, 002 ε-greedy P-B-OE 0,504 ±0, 037 0,418 ±0, 016 0,875 ±0, 006 P-B-RE 0,448 ±0, 042 0,397 ±0, 014 0,860 ±0, 007 P-BSB-OE 0,480 ±0, 042 0,429 ±0, 009 0,871 ±0, 008 P-BSB-RE 0,483 ±0, 036 0,411 ±0, 009 0,877 ±0, 005 P-BUSBC-OE 0,511 ±0, 025 0,423 ±0, 008 0,878 ±0, 009 P-BUSBC-RE 0,527 ±0, 020 0,421 ±0, 007 0,882 ±0, 006 P-SB-OE 0,523 ±0, 012 0,424 ±0, 008 0,881 ±0, 004 P-SB-RE 0,529 ±0, 008 0,425 ±0, 005 0,893 ±0, 003 TS P-B-OE 0,469 ±0, 053 0,407 ±0, 016 0,843 ±0, 008 P-B-RE 0,361 ±0, 042 0,424 ±0, 009 0,847 ±0, 018 P-BSB-OE 0,520 ±0, 030 0,427 ±0, 012 0,882 ±0, 006 P-BSB-RE 0,498 ±0, 025 0,422 ±0, 006 0,872 ±0, 005 P-BUSBC-OE 0,533 ±0, 023 0,427 ±0, 011 0,865 ±0, 008 P-BUSBC-RE 0,507 ±0, 030 0,443 ±0, 005 0,878 ±0, 011 P-SB-OE 0,531 ±0, 007 0,420 ±0, 005 0,843 ±0, 006 P-SB-RE 0,548 ±0, 007 0,424 ±0, 002 0,888 ±0, 003 UCB P-B-OE 0,547 ±0, 007 0,433 ±0, 007 0,858 ±0, 008 P-B-RE 0,491 ±0, 021 0,395 ±0, 005 0,777 ±0, 005 P-BSB-OE 0,534 ±0, 018 0,422 ±0, 005 0,821 ±0, 007 P-BSB-RE 0,500 ±0, 015 0,398 ±0, 003 0,784 ±0, 003 P-BUSBC-OE 0,545 ±0, 008 0,421 ±0, 006 0,846 ±0, 006 P-BUSBC-RE 0,505 ±0, 018 0,404 ±0, 005 0,826 ±0, 005 P-SB-OE 0,510 ±0, 008 0,401 ±0, 006 0,754 ±0, 004 P-SB-RE 0,503 ±0, 005 0,384 ±0, 004 0,714 ±0, 003 UCB2 P-B-OE 0,517 ±0, 033 0,174 ±0, 007 0,867 ±0, 006 P-B-RE 0,344 ±0, 054 0,173 ±0, 007 0,849 ±0, 010 P-BSB-OE 0,512 ±0, 014 0,170 ±0, 005 0,842 ±0, 011 P-BSB-RE 0,431 ±0, 048 0,178 ±0, 004 0,852 ±0, 006 P-BUSBC-OE 0,508 ±0, 023 0,175 ±0, 003 0,863 ±0, 014 P-BUSBC-RE 0,466 ±0, 031 0,176 ±0, 006 0,875 ±0, 003 P-SB-OE 0,467 ±0, 034 0,174 ±0, 002 0,805 ±0, 016 P-SB-RE 0,473 ±0, 005 0,178 ±0, 004 0,857 ±0, 005

Table 3: Results under Partial-vector setup, best in bold, second in italic

Summary of Experimental Results

Full feedback vector: Table 2 presents the global accuracy obtained by each algorithm on each dataset, depending on the Reward Computing process employed. Almost all of those results are significantly different (p-value < 0.05).

Most of the non-significant differences are observed between the FV-BSB-/ and FV-B-/ feedback strategies, extracted from the literature. We can see that UCB1 and UCB2 algorithms reach higher global accuracy when using the proposed BUSBC Reward Computing process. Figure 1 confirms that BUSBC outperforms the concurring approaches after a few iterations till end of the horizon. Another point of interest it that while BUSBC has not been designed to enhanced the performances of greedy or bayesian algorithms, it still allows their second best results on each dataset.

Partial feedback vector: Table 3 presents the global accuracy obtained by each algorithm on each dataset, depending on the Reward Computing and Feedback Identification processes applied. The differences between the studied Reward Computing are smaller but still significant (p-value < 0.05). This can be explained by the feedback reduction leading to a closer behavior between the studied approaches. Concerning Feedback Identification process, we also observe an impact on the global accuracy of the COM-MAB algorithm with OE outperforming RE most of the time. Note that the Bandit Rewards Computing (B) process is more competitive under a partial-vector setup than under the full-vector setup, becoming the best choice for UCB1 when applied with OE. This is mainly explained by the decrease of the number of unexpected rewarded arms. However, from the global accuracy evolution, we observed that, for both UCB1 and UCB2 algorithms and for each dataset, P-BUSBC-OE was becoming increasingly equivalent to P-B-OE . Hence, P-BUSBC-OE may, in fact, be a better choice when considering a greater horizon or when more feedback are allowed at each round. To top it all, an important point to note is that on this setting, the evaluation of the Rewards Computing processes is 1) restricted by the small number of feedbacks provided; 2) influenced by the Feedback Identification process employed. When averaging the results obtained with each Reward Computing process, that is, indepently from the Feedback Identification process employed, BUSBC actually still performs better than the Bandit (B) strategy with UCB1 and UCB2 for all datasets.

Discussion: The general feedback strategy model proposed in this article is defined as the application of three processes: a) Feedback Identification ; b) Feedback Retrieval ; c) Reward Computing. Based on our results, we observe that both the Feedback Identification and Reward Computing processes have a significant impact on the global accuracy. As the interest of the Feedback Retrieval process has previously been highlighted in the literature with Cascading Bandits models, we can conclude that any step of our general model can be used to significantly enhance the performances of a COM-MAB algorithm. A limitation of this study is the number of feedback employed under a partialsetup. The behaviors of the considered Reward Computing processes become increasingly closer as the number of perceived feedback become smaller. Similarly, with less feedback to identify, the impact observed from different Feedback Identification processes will also be smaller. In this study, since the number of feedback employed would be dependant of the application, we considered the worst case enabling differences between those approaches to ensure that the observed differences between each of the Reward Computing and Feedback Identification processes studied will be greater in real-world applications.

Conclusion

In this paper, we have formally defined a three-process model for feedback strategy and have empirically shown that for any COM-MAB algorithm, global accuracy can be improved by tuning any of those three processes. We proposed the BUSBC approach for the Reward Computing process, which gives significantly better results for UCB-based algorithms, without adding any constraint compared to previous methods. Opposing most of recents works, this paper only considers background algorithms and feedback strategies without considering any problem-dependant settings or optimizations (e.g. context availability). Our motivations were two-fold : 1) Showing that feedbacks strategies could be used to improve COM-MAB alorithms performances even on worst case scenario, i.e. when only items index and users' feedbacks can be used and thus only minute changes are possible ; 2) Illustrating benefits that can be extended to state of the art approaches built-upon the underlying COM-MAB algorithms studied. Hence, we believe that any recommender system, built-upon COM-MAB algorithms can benefit from this work. We also observed that the optimal feedback strategy for a COM-MAB algorithm may change over time, one of the promising perspectives would thus be to implement a portfolio-based algorithm to dynamically select different processes during the exploitation step.

Figure 1 :

 1 Figure 1: Global accuracy's evolution on MovieLens dataset under full-vector setup

  Algorithm 1 P-BUSBC-OE Require: S t , Recommended Super arm. Y t , Feedback vector associated to A or user u t . π, Agent's policy. ψ, Number of feedback allowed.

	3:	Construct P t with
		P t = P t ∪ {argmin a∈St\Pt obs a,t }
		(according to Equation 2)
	4: end while
	5: Feedback Retrieval: F t = {Y t,a | a ∈ P t }
	6: Compute cumulative reward: R B t = P ⊤ t F t
	7: for a ∈ P t do
	8:	if F t,a > 0 then
	9:	Update policy π with SR t,a = SR t-1,a + R B t
	10:	end if
	11: end for
		4 Experiments
	4.1 Experiment Settings

1: P t ← ∅ 2: while |P t | < ψ do Datasets: Experiments are performed on several real-life datasets: RSASM, Jester and MovieLens (See Table

Table 1 :

 1 Datasets

	Datasets	Users Arms Interactions	Source
	RSASM	2 152	18	> 38K	Kaggle
	Jester	59 132	150	> 1.7M	Kaggle
	MovieLens	942	1682	> 100K	Groupelens.org

Table 2 :

 2 Results under Full-vector setup, best in bold, second in italic

To internally compute a cumulative reward, the Bandit strategy needs a reward vector equivalent to the one used with Semi-Bandit.

Note that it is a characteristic of the original dataset.