Claire Vernade

Onno Eberhard, Claire Vernade, Michael Muehlebach

Reinforcement learning algorithms are commonly analyzed (and designed) under the Markov assumption. This is unrealistic, as most environments encountered in practice are either partially observable, or require function approximation that restricts the agent to access non-Markovian state features. We consider the problem of learning an optimal reactive policy in a finite environment with deterministic observations (or equivalently, hard state aggregation). We introduce a new algorithm, Committed Q-learning, and prove almost-sure convergence to the optimal reactive policy under an intuitive assumption we call rewire-robustness. This assumption is strictly weaker than the $q_\star$-realizability condition used in prior work. Our algorithm is a variant of classical Q-learning in which the behavior policy commits to a single action upon entering a feature, and only resamples actions when the observed feature changes. A crucial part of our analysis is the introduction of quasi-Markov environments.

Alexandre Marthe, Aurélien Garivier, Claire Vernade

What are the functionals of the reward that can be computed and optimized exactly in Markov Decision Processes?In the finite-horizon, undiscounted setting, Dynamic Programming (DP) can only handle these operations efficiently for certain classes of statistics. We summarize the characterization of these classes for policy evaluation, and give a new answer for the planning problem. Interestingly, we prove that only generalized means can be optimized exactly, even in the more general framework of Distributional Reinforcement Learning (DistRL).DistRL permits, however, to evaluate other functionals approximately. We provide error bounds on the resulting estimators, and discuss the potential of this approach as well as its limitations.These results contribute to advancing the theory of Markov Decision Processes by examining overall characteristics of the return, and particularly risk-conscious strategies.

Khimya Khetarpal, Claire Vernade, Brendan O'Donoghue et al.

We study the problem of planning under model uncertainty in an online meta-reinforcement learning (RL) setting where an agent is presented with a sequence of related tasks with limited interactions per task. The agent can use its experience in each task and across tasks to estimate both the transition model and the distribution over tasks. We propose an algorithm to meta-learn the underlying structure across tasks, utilize it to plan in each task, and upper-bound the regret of the planning loss. Our bound suggests that the average regret over tasks decreases as the number of tasks increases and as the tasks are more similar. In the classical single-task setting, it is known that the planning horizon should depend on the estimated model's accuracy, that is, on the number of samples within task. We generalize this finding to meta-RL and study this dependence of planning horizons on the number of tasks. Based on our theoretical findings, we derive heuristics for selecting slowly increasing discount factors, and we validate its significance empirically.

Mirabel Reid, Tom Sühr, Claire Vernade et al.

Machine Learning (ML) models are increasingly used to support or substitute decision making. In applications where skilled experts are a limited resource, it is crucial to reduce their burden and automate decisions when the performance of an ML model is at least of equal quality. However, models are often pre-trained and fixed, while tasks arrive sequentially and their distribution may shift. In that case, the respective performance of the decision makers may change, and the deferral algorithm must remain adaptive. We propose a contextual bandit model of this online decision making problem. Our framework includes budget constraints and different types of partial feedback models. Beyond the theoretical guarantees of our algorithm, we propose efficient extensions that achieve remarkable performance on real-world datasets.

Amir Rezaei Balef, Claire Vernade, Katharina Eggensperger

The Combined Algorithm Selection and Hyperparameter optimization (CASH) is a challenging resource allocation problem in the field of AutoML. We propose MaxUCB, a max k-armed bandit method to trade off exploring different model classes and conducting hyperparameter optimization. MaxUCB is specifically designed for the light-tailed and bounded reward distributions arising in this setting and, thus, provides an efficient alternative compared to classic max k-armed bandit methods assuming heavy-tailed reward distributions. We theoretically and empirically evaluate our method on four standard AutoML benchmarks, demonstrating superior performance over prior approaches. We make our code and data available at https://github.com/amirbalef/CASH_with_Bandits

Amer Essakine, Claire Vernade

We study best-policy identification for finite-horizon risk-sensitive reinforcement learning under the entropic risk measure. Recent work established a constant gap in the exponential horizon dependence between lower and upper bounds on the number of samples required to identify an approximately optimal policy. Precisely, known lower bounds scale in $Ω(e^{|β| H})$ where $H$ is the horizon of the MDP, while the state-of-the-art upper bound achieves at best $O(e^{2|β| H})$ (arXiv:2506.00286v2) using a generative model. We show that this extra exponential factor can be traced to overly loose concentration control for exponential utilities. To close this open gap, we revisit the analysis of this problem through a forward-model based algorithm building on KL-based exploration bonuses that we adapt to the entropic criterion. The improvement we get is due to two main novel technical innovations. We leverage the smoothness properties of the exponential utility to derive sharper concentration bounds, and we propose a new stopping rule that exploits further this tightness to obtain a sample complexity that matches the lower bound.

Ziyad Sheebaelhamd, Luca Viano, Volkan Cevher et al.

This work investigates multi-objective imitation learning: the problem of recovering policies that lie on the Pareto front given demonstrations from multiple Pareto-optimal experts in a Multi-Objective Markov Decision Process (MOMDP). Standard imitation approaches are ill-equipped for this regime, as naively aggregating conflicting expert trajectories can result in dominated policies. To address this, we introduce Multi-Output Augmented Behavioral Cloning (MA-BC), an algorithm that systematically partitions divergent expert data while pooling state-action pairs where no behavior conflict is observed. Theoretically, we prove that MA-BC converges to Pareto-optimal policies at a faster statistical rate than any learner that considers each expert dataset independently. Furthermore, we establish a novel lower bound for multi-objective imitation learning, demonstrating that MA-BC is minimax optimal. Finally, we empirically validate our algorithm across diverse discrete environments and, guided by our theoretical insights, extend and evaluate MA-BC on a continuous Linear Quadratic Regulator (LQR) control task.

Onno Eberhard, Michael Muehlebach, Claire Vernade

Partially observable environments present a considerable computational challenge in reinforcement learning due to the need to consider long histories. Learning with a finite window of observations quickly becomes intractable as the window length grows. In this work, we introduce memory traces. Inspired by eligibility traces, these are compact representations of the history of observations in the form of exponential moving averages. We prove sample complexity bounds for the problem of offline on-policy evaluation that quantify the return errors achieved with memory traces for the class of Lipschitz continuous value estimates. We establish a close connection to the window approach, and demonstrate that, in certain environments, learning with memory traces is significantly more sample efficient. Finally, we underline the effectiveness of memory traces empirically in online reinforcement learning experiments for both value prediction and control.

Alexandre Marthe, Samuel Bounan, Aurélien Garivier et al.

Risk-sensitive planning aims to identify policies maximizing some tail-focused metrics in Markov Decision Processes (MDPs). Such an optimization task can be very costly for the most widely used and interpretable metrics such as threshold probabilities or (Conditional) Values at Risk. Indeed, previous work showed that only Entropic Risk Measures (EntRM) can be efficiently optimized through dynamic programming, leaving a hard-to-interpret parameter to choose. We show that the computation of the full set of optimal policies for EntRM across parameter values leads to tight approximations for the metrics of interest. We prove that this optimality front can be computed effectively thanks to a novel structural analysis and smoothness properties of entropic risks. Empirical results demonstrate that our approach achieves strong performance in a variety of decision-making scenarios.

Nicolas Nguyen, Imad Aouali, András György et al.

We study the problem of Bayesian fixed-budget best-arm identification (BAI) in structured bandits. We propose an algorithm that uses fixed allocations based on the prior information and the structure of the environment. We provide theoretical bounds on its performance across diverse models, including the first prior-dependent upper bounds for linear and hierarchical BAI. Our key contribution is introducing new proof methods that result in tighter bounds for multi-armed BAI compared to existing methods. We extensively compare our approach to other fixed-budget BAI methods, demonstrating its consistent and robust performance in various settings. Our work improves our understanding of Bayesian fixed-budget BAI in structured bandits and highlights the effectiveness of our approach in practical scenarios.

Nicolas Nguyen, Solenne Gaucher, Claire Vernade

We study the problem of non-stationary Lipschitz bandits, where the number of actions is infinite and the reward function, satisfying a Lipschitz assumption, can change arbitrarily over time. We design an algorithm that adaptively tracks the recently introduced notion of significant shifts, defined by large deviations of the cumulative reward function. To detect such reward changes, our algorithm leverages a hierarchical discretization of the action space. Without requiring any prior knowledge of the non-stationarity, our algorithm achieves a minimax-optimal dynamic regret bound of $\mathcal{\widetilde{O}}(\tilde{L}^{1/3}T^{2/3})$, where $\tilde{L}$ is the number of significant shifts and $T$ the horizon. This result provides the first optimal guarantee in this setting.

Ziyad Sheebaelhamd, Michael Tschannen, Michael Muehlebach et al.

Current transformer-based imitation learning approaches introduce discrete action representations and train an autoregressive transformer decoder on the resulting latent code. However, the initial quantization breaks the continuous structure of the action space thereby limiting the capabilities of the generative model. We propose a quantization-free method instead that leverages Generative Infinite-Vocabulary Transformers (GIVT) as a direct, continuous policy parametrization for autoregressive transformers. This simplifies the imitation learning pipeline while achieving state-of-the-art performance on a variety of popular simulated robotics tasks. We enhance our policy roll-outs by carefully studying sampling algorithms, further improving the results.

Simon Weissmann, Till Freihaut, Claire Vernade et al.

In the context of stochastic bandit models, this article examines how to design sample-efficient behavior policies for the importance sampling evaluation of multiple target policies. From importance sampling theory, it is well established that sample efficiency is highly sensitive to the KL divergence between the target and importance sampling distributions. We first analyze a single behavior policy defined as the KL-barycenter of the target policies. Then, we refine this approach by clustering the target policies into groups with small KL divergences and assigning each cluster its own KL-barycenter as a behavior policy. This clustered KL-based policy evaluation (CKL-PE) algorithm provides a novel perspective on optimal policy selection. We prove upper bounds on the sample complexity of our method and demonstrate its effectiveness with numerical validation.

MohammadJavad Azizi, Thang Duong, Yasin Abbasi-Yadkori et al.

We study a sequential decision problem where the learner faces a sequence of $K$-armed bandit tasks. The task boundaries might be known (the bandit meta-learning setting), or unknown (the non-stationary bandit setting). For a given integer $M\le K$, the learner aims to compete with the best subset of arms of size $M$. We design an algorithm based on a reduction to bandit submodular maximization, and show that, for $T$ rounds comprised of $N$ tasks, in the regime of large number of tasks and small number of optimal arms $M$, its regret in both settings is smaller than the simple baseline of $\tilde{O}(\sqrt{KNT})$ that can be obtained by using standard algorithms designed for non-stationary bandit problems. For the bandit meta-learning problem with fixed task length $τ$, we show that the regret of the algorithm is bounded as $\tilde{O}(NM\sqrt{M τ}+N^{2/3}Mτ)$. Under additional assumptions on the identifiability of the optimal arms in each task, we show a bandit meta-learning algorithm with an improved $\tilde{O}(N\sqrt{M τ}+N^{1/2}\sqrt{M K τ})$ regret.

Ian Gemp, Brian McWilliams, Claire Vernade et al.

We build on the recently proposed EigenGame that views eigendecomposition as a competitive game. EigenGame's updates are biased if computed using minibatches of data, which hinders convergence and more sophisticated parallelism in the stochastic setting. In this work, we propose an unbiased stochastic update that is asymptotically equivalent to EigenGame, enjoys greater parallelism allowing computation on datasets of larger sample sizes, and outperforms EigenGame in experiments. We present applications to finding the principal components of massive datasets and performing spectral clustering of graphs. We analyze and discuss our proposed update in the context of EigenGame and the shift in perspective from optimization to games.

Johannes Kirschner, Tor Lattimore, Claire Vernade et al.

We introduce a simple and efficient algorithm for stochastic linear bandits with finitely many actions that is asymptotically optimal and (nearly) worst-case optimal in finite time. The approach is based on the frequentist information-directed sampling (IDS) framework, with a surrogate for the information gain that is informed by the optimization problem that defines the asymptotic lower bound. Our analysis sheds light on how IDS balances the trade-off between regret and information and uncovers a surprising connection between the recently proposed primal-dual methods and the IDS algorithm. We demonstrate empirically that IDS is competitive with UCB in finite-time, and can be significantly better in the asymptotic regime.

Alexandra Carpentier, Claire Vernade, Yasin Abbasi-Yadkori

This note proposes a new proof and new perspectives on the so-called Elliptical Potential Lemma. This result is important in online learning, especially for linear stochastic bandits. The original proof of the result, however short and elegant, does not give much flexibility on the type of potentials considered and we believe that this new interpretation can be of interest for future research in this field.

Ian Gemp, Brian McWilliams, Claire Vernade et al.

We present a novel view on principal component analysis (PCA) as a competitive game in which each approximate eigenvector is controlled by a player whose goal is to maximize their own utility function. We analyze the properties of this PCA game and the behavior of its gradient based updates. The resulting algorithm -- which combines elements from Oja's rule with a generalized Gram-Schmidt orthogonalization -- is naturally decentralized and hence parallelizable through message passing. We demonstrate the scalability of the algorithm with experiments on large image datasets and neural network activations. We discuss how this new view of PCA as a differentiable game can lead to further algorithmic developments and insights.

Ilja Kuzborskij, Claire Vernade, András György et al.

We consider off-policy evaluation in the contextual bandit setting for the purpose of obtaining a robust off-policy selection strategy, where the selection strategy is evaluated based on the value of the chosen policy in a set of proposal (target) policies. We propose a new method to compute a lower bound on the value of an arbitrary target policy given some logged data in contextual bandits for a desired coverage. The lower bound is built around the so-called Self-normalized Importance Weighting (SN) estimator. It combines the use of a semi-empirical Efron-Stein tail inequality to control the concentration and a new multiplicative (rather than additive) control of the bias. The new approach is evaluated on a number of synthetic and real datasets and is found to be superior to its main competitors, both in terms of tightness of the confidence intervals and the quality of the policies chosen.

Anne Gael Manegueu, Claire Vernade, Alexandra Carpentier et al.

Significant work has been recently dedicated to the stochastic delayed bandit setting because of its relevance in applications. The applicability of existing algorithms is however restricted by the fact that strong assumptions are often made on the delay distributions, such as full observability, restrictive shape constraints, or uniformity over arms. In this work, we weaken them significantly and only assume that there is a bound on the tail of the delay. In particular, we cover the important case where the delay distributions vary across arms, and the case where the delays are heavy-tailed. Addressing these difficulties, we propose a simple but efficient UCB-based algorithm called the PatientBandits. We provide both problems-dependent and problems-independent bounds on the regret as well as performance lower bounds.

Claire Vernade, Andras Gyorgy, Timothy Mann

Online recommender systems often face long delays in receiving feedback, especially when optimizing for some long-term metrics. While mitigating the effects of delays in learning is well-understood in stationary environments, the problem becomes much more challenging when the environment changes. In fact, if the timescale of the change is comparable to the delay, it is impossible to learn about the environment, since the available observations are already obsolete. However, the arising issues can be addressed if intermediate signals are available without delay, such that given those signals, the long-term behavior of the system is stationary. To model this situation, we introduce the problem of stochastic, non-stationary, delayed bandits with intermediate observations. We develop a computationally efficient algorithm based on UCRL, and prove sublinear regret guarantees for its performance. Experimental results demonstrate that our method is able to learn in non-stationary delayed environments where existing methods fail.

Cindy Trinh, Emilie Kaufmann, Claire Vernade et al.

Stochastic Rank-One Bandits (Katarya et al, (2017a,b)) are a simple framework for regret minimization problems over rank-one matrices of arms. The initially proposed algorithms are proved to have logarithmic regret, but do not match the existing lower bound for this problem. We close this gap by first proving that rank-one bandits are a particular instance of unimodal bandits, and then providing a new analysis of Unimodal Thompson Sampling (UTS), initially proposed by Paladino et al (2017). We prove an asymptotically optimal regret bound on the frequentist regret of UTS and we support our claims with simulations showing the significant improvement of our method compared to the state-of-the-art.

Yoan Russac, Claire Vernade, Olivier Cappé

We consider a stochastic linear bandit model in which the available actions correspond to arbitrary context vectors whose associated rewards follow a non-stationary linear regression model. In this setting, the unknown regression parameter is allowed to vary in time. To address this problem, we propose D-LinUCB, a novel optimistic algorithm based on discounted linear regression, where exponential weights are used to smoothly forget the past. This involves studying the deviations of the sequential weighted least-squares estimator under generic assumptions. As a by-product, we obtain novel deviation results that can be used beyond non-stationary environments. We provide theoretical guarantees on the behavior of D-LinUCB in both slowly-varying and abruptly-changing environments. We obtain an upper bound on the dynamic regret that is of order d^{2/3} B\_T^{1/3}T^{2/3}, where B\_T is a measure of non-stationarity (d and T being, respectively, dimension and horizon). This rate is known to be optimal. We also illustrate the empirical performance of D-LinUCB and compare it with recently proposed alternatives in simulated environments.

Claire Vernade, Alexandra Carpentier, Tor Lattimore et al.

Stochastic linear bandits are a natural and well-studied model for structured exploration/exploitation problems and are widely used in applications such as online marketing and recommendation. One of the main challenges faced by practitioners hoping to apply existing algorithms is that usually the feedback is randomly delayed and delays are only partially observable. For example, while a purchase is usually observable some time after the display, the decision of not buying is never explicitly sent to the system. In other words, the learner only observes delayed positive events. We formalize this problem as a novel stochastic delayed linear bandit and propose ${\tt OTFLinUCB}$ and ${\tt OTFLinTS}$, two computationally efficient algorithms able to integrate new information as it becomes available and to deal with the permanently censored feedback. We prove optimal $\tilde O(\smash{d\sqrt{T}})$ bounds on the regret of the first algorithm and study the dependency on delay-dependent parameters. Our model, assumptions and results are validated by experiments on simulated and real data.

Mastane Achab, Stephan Clémençon, Aurélien Garivier et al.

This paper is devoted to the study of the max K-armed bandit problem, which consists in sequentially allocating resources in order to detect extreme values. Our contribution is twofold. We first significantly refine the analysis of the ExtremeHunter algorithm carried out in Carpentier and Valko (2014), and next propose an alternative approach, showing that, remarkably, Extreme Bandits can be reduced to a classical version of the bandit problem to a certain extent. Beyond the formal analysis, these two approaches are compared through numerical experiments.

Claire Vernade, Olivier Cappé, Vianney Perchet

Online advertising and product recommendation are important domains of applications for multi-armed bandit methods. In these fields, the reward that is immediately available is most often only a proxy for the actual outcome of interest, which we refer to as a conversion. For instance, in web advertising, clicks can be observed within a few seconds after an ad display but the corresponding sale --if any-- will take hours, if not days to happen. This paper proposes and investigates a new stochas-tic multi-armed bandit model in the framework proposed by Chapelle (2014) --based on empirical studies in the field of web advertising-- in which each action may trigger a future reward that will then happen with a stochas-tic delay. We assume that the probability of conversion associated with each action is unknown while the distribution of the conversion delay is known, distinguishing between the (idealized) case where the conversion events may be observed whatever their delay and the more realistic setting in which late conversions are censored. We provide performance lower bounds as well as two simple but efficient algorithms based on the UCB and KLUCB frameworks. The latter algorithm, which is preferable when conversion rates are low, is based on a Poissonization argument, of independent interest in other settings where aggregation of Bernoulli observations with different success probabilities is required.

Joon Kwon, Vianney Perchet, Claire Vernade

In the classical multi-armed bandit problem, d arms are available to the decision maker who pulls them sequentially in order to maximize his cumulative reward. Guarantees can be obtained on a relative quantity called regret, which scales linearly with d (or with sqrt(d) in the minimax sense). We here consider the sparse case of this classical problem in the sense that only a small number of arms, namely s < d, have a positive expected reward. We are able to leverage this additional assumption to provide an algorithm whose regret scales with s instead of d. Moreover, we prove that this algorithm is optimal by providing a matching lower bound - at least for a wide and pertinent range of parameters that we determine - and by evaluating its performance on simulated data.

Sumeet Katariya, Branislav Kveton, Csaba Szepesvári et al.

The probability that a user will click a search result depends both on its relevance and its position on the results page. The position based model explains this behavior by ascribing to every item an attraction probability, and to every position an examination probability. To be clicked, a result must be both attractive and examined. The probabilities of an item-position pair being clicked thus form the entries of a rank-$1$ matrix. We propose the learning problem of a Bernoulli rank-$1$ bandit where at each step, the learning agent chooses a pair of row and column arms, and receives the product of their Bernoulli-distributed values as a reward. This is a special case of the stochastic rank-$1$ bandit problem considered in recent work that proposed an elimination based algorithm Rank1Elim, and showed that Rank1Elim's regret scales linearly with the number of rows and columns on "benign" instances. These are the instances where the minimum of the average row and column rewards $μ$ is bounded away from zero. The issue with Rank1Elim is that it fails to be competitive with straightforward bandit strategies as $μ\rightarrow 0$. In this paper we propose Rank1ElimKL which simply replaces the (crude) confidence intervals of Rank1Elim with confidence intervals based on Kullback-Leibler (KL) divergences, and with the help of a novel result concerning the scaling of KL divergences we prove that with this change, our algorithm will be competitive no matter the value of $μ$. Experiments with synthetic data confirm that on benign instances the performance of Rank1ElimKL is significantly better than that of even Rank1Elim, while experiments with models derived from real data confirm that the improvements are significant across the board, regardless of whether the data is benign or not.

Sumeet Katariya, Branislav Kveton, Csaba Szepesvari et al.

We propose stochastic rank-$1$ bandits, a class of online learning problems where at each step a learning agent chooses a pair of row and column arms, and receives the product of their values as a reward. The main challenge of the problem is that the individual values of the row and column are unobserved. We assume that these values are stochastic and drawn independently. We propose a computationally-efficient algorithm for solving our problem, which we call Rank1Elim. We derive a $O((K + L) (1 / Δ) \log n)$ upper bound on its $n$-step regret, where $K$ is the number of rows, $L$ is the number of columns, and $Δ$ is the minimum of the row and column gaps; under the assumption that the mean row and column rewards are bounded away from zero. To the best of our knowledge, we present the first bandit algorithm that finds the maximum entry of a rank-$1$ matrix whose regret is linear in $K + L$, $1 / Δ$, and $\log n$. We also derive a nearly matching lower bound. Finally, we evaluate Rank1Elim empirically on multiple problems. We observe that it leverages the structure of our problems and can learn near-optimal solutions even if our modeling assumptions are mildly violated.

Paul Lagrée, Claire Vernade, Olivier Cappé

Sequentially learning to place items in multi-position displays or lists is a task that can be cast into the multiple-play semi-bandit setting. However, a major concern in this context is when the system cannot decide whether the user feedback for each item is actually exploitable. Indeed, much of the content may have been simply ignored by the user. The present work proposes to exploit available information regarding the display position bias under the so-called Position-based click model (PBM). We first discuss how this model differs from the Cascade model and its variants considered in several recent works on multiple-play bandits. We then provide a novel regret lower bound for this model as well as computationally efficient algorithms that display good empirical and theoretical performance.

Hossein Vahabi, Paul Lagrée, Claire Vernade et al.

In many web applications, a recommendation is not a single item suggested to a user but a list of possibly interesting contents that may be ranked in some contexts. The combinatorial bandit problem has been studied quite extensively these last two years and many theoretical results now exist : lower bounds on the regret or asymptotically optimal algorithms. However, because of the variety of situations that can be considered, results are designed to solve the problem for a specific reward structure such as the Cascade Model. The present work focuses on the problem of ranking items when the user is allowed to click on several items while scanning the list from top to bottom.

Claire Vernade, Olivier Cappé

Recommending items to users is a challenging task due to the large amount of missing information. In many cases, the data solely consist of ratings or tags voluntarily contributed by each user on a very limited subset of the available items, so that most of the data of potential interest is actually missing. Current approaches to recommendation usually assume that the unobserved data is missing at random. In this contribution, we provide statistical evidence that existing movie recommendation datasets reveal a significant positive association between the rating of items and the propensity to select these items. We propose a computationally efficient variational approach that makes it possible to exploit this selection bias so as to improve the estimation of ratings from small populations of users. Results obtained with this approach applied to neighborhood-based collaborative filtering illustrate its potential for improving the reliability of the recommendation.