arXiv subjects

Odalric-Ambrym Maillard

Publications and source records attributed to Odalric-Ambrym Maillard.

At least 19 recordsLinked to original sources

arXiv2026

Information-Based Exploration via Random Features for Reinforcement Learning

Representation learning has enabled classical exploration strategies to be extended to deep Reinforcement Learning (RL), but often makes algorithms more complex and theoretical guarantees harder to establish. We introduce Random Feature Information Gain (RFIG), grounded in Bayesian kernel methods theory, which uses random Fourier features to approximate information gain and compute exploration bonuses in non-countable spaces. We provide error bounds on information gain approximation and avoid the black-box aspects of neural network-based uncertainty estimation, for optimism-based exploration. We present practical details that make RFIG scalable to deep RL scenarios, enabling smooth integration into standard deep RL algorithms. Experimental evaluation across diverse control and navigation tasks demonstrates that RFIG achieves competitive performance with well-established deep exploration methods while offering superior theoretical interpretation.

cs.LG↗

arXiv2026

Bandits for Efficient Experimentation: Adapting to Control Group, Preferences, and Context Drifts

We consider a variant of the linear contextual stochastic multi-armed bandits, where the learner must provide recommendations to a group of users, each having its personalized preference vector, and in the presence of context distributions that are drifting over time. Under practitioner-friendly assumptions, we reduce this setting to linear bandit with stationary mean but heteroskedastic and non-stationary noise. We further study the case when the learner must ensure the mean reward of each decision must exceed that of a baseline strategy $\boldsymbolπ_0$ at each decision step. We introduce Dri-MED, an algorithm inspired from the linear version of the MED strategy, and carefully adapted to handle the non-stationary heteroskedastic noise. We show that the instance-dependent regret scales as $\tilde{\mathcal O}\left(\fracκ{\tildeΔ}d^2(\log(T)\right)$, where $\tildeΔ$ is the constraint-aware sub-optimality gap subject to policy $π_0$, with variance-aware multiplicative term $κ$ that we carefully handle using heteroskedastic regression. We further show Dri-MED enjoys $\tilde{\mathcal{O}}(d)$ expected constraint violations. Our numerical results suggest that Dri-MED significantly outperforms conservative baselines that ignores the drift and preference structure.

cs.LG↗

arXiv2026

Pliable rejection sampling

Rejection sampling is a technique for sampling from difficult distributions. However, its use is limited due to a high rejection rate. Common adaptive rejection sampling methods either work only for very specific distributions or without performance guarantees. In this paper, we present pliable rejection sampling (PRS), a new approach to rejection sampling, where we learn the sampling proposal using a kernel estimator. Since our method builds on rejection sampling, the samples obtained are with high probability i.i.d. and distributed according to f. Moreover, PRS comes with a guarantee on the number of accepted samples.

stat.ML↗

arXiv2026

Hierarchical Subspaces of Policies for Continual Offline Reinforcement Learning

We consider a Continual Reinforcement Learning setup, where a learning agent must continuously adapt to new tasks while retaining previously acquired skill sets, with a focus on the challenge of avoiding forgetting past gathered knowledge and ensuring scalability with the growing number of tasks. Such issues prevail in autonomous robotics and video game simulations, notably for navigation tasks prone to topological or kinematic changes. To address these issues, we introduce HiSPO, a novel hierarchical framework designed specifically for continual learning in navigation settings from offline data. Our method leverages distinct policy subspaces of neural networks to enable flexible and efficient adaptation to new tasks while preserving existing knowledge. We demonstrate, through a careful experimental study, the effectiveness of our method in both classical MuJoCo maze environments and complex video game-like navigation simulations, showcasing competitive performances and satisfying adaptability with respect to classical continual learning metrics, in particular regarding the memory usage and efficiency.

cs.LG↗

arXiv2026

A Continual Offline Reinforcement Learning Benchmark for Navigation Tasks

Autonomous agents operating in domains such as robotics or video game simulations must adapt to changing tasks without forgetting about the previous ones. This process called Continual Reinforcement Learning poses non-trivial difficulties, from preventing catastrophic forgetting to ensuring the scalability of the approaches considered. Building on recent advances, we introduce a benchmark providing a suite of video-game navigation scenarios, thus filling a gap in the literature and capturing key challenges : catastrophic forgetting, task adaptation, and memory efficiency. We define a set of various tasks and datasets, evaluation protocols, and metrics to assess the performance of algorithms, including state-of-the-art baselines. Our benchmark is designed not only to foster reproducible research and to accelerate progress in continual reinforcement learning for gaming, but also to provide a reproducible framework for production pipelines -- helping practitioners to identify and to apply effective approaches.

cs.LG↗

arXiv2026

Offline Goal-Conditioned Reinforcement Learning with Projective Quasimetric Planning

Offline Goal-Conditioned Reinforcement Learning seeks to train agents to reach specified goals from previously collected trajectories. Scaling that promises to long-horizon tasks remains challenging, notably due to compounding value-estimation errors. Principled geometric offers a potential solution to address these issues. Following this insight, we introduce Projective Quasimetric Planning (ProQ), a compositional framework that learns an asymmetric distance and then repurposes it, firstly as a repulsive energy forcing a sparse set of keypoints to uniformly spread over the learned latent space, and secondly as a structured directional cost guiding towards proximal sub-goals. In particular, ProQ couples this geometry with a Lagrangian out-of-distribution detector to ensure the learned keypoints stay within reachable areas. By unifying metric learning, keypoint coverage, and goal-conditioned control, our approach produces meaningful sub-goals and robustly drives long-horizon goal-reaching on diverse a navigation benchmarks.

cs.LG↗

arXiv2025

How Hard is it to Confuse a World Model?

In reinforcement learning (RL) theory, the concept of most confusing instances is central to establishing regret lower bounds, that is, the minimal exploration needed to solve a problem. Given a reference model and its optimal policy, a most confusing instance is the statistically closest alternative model that makes a suboptimal policy optimal. While this concept is well-studied in multi-armed bandits and ergodic tabular Markov decision processes, constructing such instances remains an open question in the general case. In this paper, we formalize this problem for neural network world models as a constrained optimization: finding a modified model that is statistically close to the reference one, while producing divergent performance between optimal and suboptimal policies. We propose an adversarial training procedure to solve this problem and conduct an empirical study across world models of varying quality. Our results suggest that the degree of achievable confusion correlates with uncertainty in the approximate model, which may inform theoretically-grounded exploration strategies for deep model-based RL.

cs.LG↗

arXiv2025

The Confusing Instance Principle for Online Linear Quadratic Control

We revisit the problem of controlling linear systems with quadratic cost under unknown dynamics with model-based reinforcement learning. Traditional methods like Optimism in the Face of Uncertainty and Thompson Sampling, rooted in multi-armed bandits (MABs), face practical limitations. In contrast, we propose an alternative based on the Confusing Instance (CI) principle, which underpins regret lower bounds in MABs and discrete Markov Decision Processes (MDPs) and is central to the Minimum Empirical Divergence (MED) family of algorithms, known for their asymptotic optimality in various settings. By leveraging the structure of LQR policies along with sensitivity and stability analysis, we develop MED-LQ. This novel control strategy extends the principles of CI and MED beyond small-scale settings. Our benchmarks on a comprehensive control suite demonstrate that MED-LQ achieves competitive performance in various scenarios while highlighting its potential for broader applications in large-scale MDPs.

cs.LG↗

arXiv2025

Asymptotically Optimal Problem-Dependent Bandit Policies for Transfer Learning

We study the non-contextual multi-armed bandit problem in a transfer learning setting: before any pulls, the learner is given N'_k i.i.d. samples from each source distribution nu'_k, and the true target distributions nu_k lie within a known distance bound d_k(nu_k, nu'_k) <= L_k. In this framework, we first derive a problem-dependent asymptotic lower bound on cumulative regret that extends the classical Lai-Robbins result to incorporate the transfer parameters (d_k, L_k, N'_k). We then propose KL-UCB-Transfer, a simple index policy that matches this new bound in the Gaussian case. Finally, we validate our approach via simulations, showing that KL-UCB-Transfer significantly outperforms the no-prior baseline when source and target distributions are sufficiently close.

cs.LG↗

arXiv2025

Leveraging priors on distribution functions for multi-arm bandits

We introduce Dirichlet Process Posterior Sampling (DPPS), a Bayesian non-parametric algorithm for multi-arm bandits based on Dirichlet Process (DP) priors. Like Thompson-sampling, DPPS is a probability-matching algorithm, i.e., it plays an arm based on its posterior-probability of being optimal. Instead of assuming a parametric class for the reward generating distribution of each arm, and then putting a prior on the parameters, in DPPS the reward generating distribution is directly modeled using DP priors. DPPS provides a principled approach to incorporate prior belief about the bandit environment, and in the noninformative limit of the DP posteriors (i.e. Bayesian Bootstrap), we recover Non Parametric Thompson Sampling (NPTS), a popular non-parametric bandit algorithm, as a special case of DPPS. We employ stick-breaking representation of the DP priors, and show excellent empirical performance of DPPS in challenging synthetic and real world bandit environments. Finally, using an information-theoretic analysis, we show non-asymptotic optimality of DPPS in the Bayesian regret setup.

stat.ML↗

arXiv2025

The regret lower bound for communicating Markov Decision Processes

This paper is devoted to the extension of the regret lower bound beyond ergodic Markov decision processes (MDPs) in the problem dependent setting. While the regret lower bound for ergodic MDPs is well-known and reached by tractable algorithms, we prove that the regret lower bound becomes significatively more complex in communicating MDPs. Our lower bound revisits the necessary explorative behavior of consistent learning agents and further explains that all optimal regions of the environment must be overvisited compared to sub-optimal ones, a phenomenon that we refer to as co-exploration. In tandem, we show that these two explorative and co-explorative behaviors are intertwined with navigation constraints obtained by scrutinizing the navigation structure at logarithmic scale. The resulting lower bound is expressed as the solution of an optimization problem that, in many standard classes of MDPs, can be specialized to recover existing results. From a computational perspective, it is provably $Σ_2^\textrm{P}$-hard in general and as a matter of fact, even testing the membership to the feasible region is coNP-hard. We further provide an algorithm to approximate the lower bound in a constructive way.

cs.LG↗

arXiv2025

Kriging and Gaussian Process Interpolation for Georeferenced Data Augmentation

Data augmentation is a crucial step in the development of robust supervised learning models, especially when dealing with limited datasets. This study explores interpolation techniques for the augmentation of geo-referenced data, with the aim of predicting the presence of Commelina benghalensis L. in sugarcane plots in La R{é}union. Given the spatial nature of the data and the high cost of data collection, we evaluated two interpolation approaches: Gaussian processes (GPs) with different kernels and kriging with various variograms. The objectives of this work are threefold: (i) to identify which interpolation methods offer the best predictive performance for various regression algorithms, (ii) to analyze the evolution of performance as a function of the number of observations added, and (iii) to assess the spatial consistency of augmented datasets. The results show that GP-based methods, in particular with combined kernels (GP-COMB), significantly improve the performance of regression algorithms while requiring less additional data. Although kriging shows slightly lower performance, it is distinguished by a more homogeneous spatial coverage, a potential advantage in certain contexts.

cs.AI↗

arXiv2025

Interpolation pour l'augmentation de donnees : Application à la gestion des adventices de la canne a sucre a la Reunion

Data augmentation is a crucial step in the development of robust supervised learning models, especially when dealing with limited datasets. This study explores interpolation techniques for the augmentation of geo-referenced data, with the aim of predicting the presence of Commelina benghalensis L. in sugarcane plots in La Réunion. Given the spatial nature of the data and the high cost of data collection, we evaluated two interpolation approaches: Gaussian processes (GPs) with different kernels and kriging with various variograms. The objectives of this work are threefold: (i) to identify which interpolation methods offer the best predictive performance for various regression algorithms, (ii) to analyze the evolution of performance as a function of the number of observations added, and (iii) to assess the spatial consistency of augmented datasets. The results show that GP-based methods, in particular with combined kernels (GP-COMB), significantly improve the performance of regression algorithms while requiring less additional data. Although kriging shows slightly lower performance, it is distinguished by a more homogeneous spatial coverage, a potential advantage in certain contexts.

q-bio.QM↗

arXiv2024

Provably Efficient Exploration in Reward Machines with Low Regret

We study reinforcement learning (RL) for decision processes with non-Markovian reward, in which high-level knowledge of the task in the form of reward machines is available to the learner. We consider probabilistic reward machines with initially unknown dynamics, and investigate RL under the average-reward criterion, where the learning performance is assessed through the notion of regret. Our main algorithmic contribution is a model-based RL algorithm for decision processes involving probabilistic reward machines that is capable of exploiting the structure induced by such machines. We further derive high-probability and non-asymptotic bounds on its regret and demonstrate the gain in terms of regret over existing algorithms that could be applied, but obliviously to the structure. We also present a regret lower bound for the studied setting. To the best of our knowledge, the proposed algorithm constitutes the first attempt to tailor and analyze regret specifically for RL with probabilistic reward machines.

cs.LG↗

arXiv2024

AdaStop: adaptive statistical testing for sound comparisons of Deep RL agents

Recently, the scientific community has questioned the statistical reproducibility of many empirical results, especially in the field of machine learning. To contribute to the resolution of this reproducibility crisis, we propose a theoretically sound methodology for comparing the performance of a set of algorithms. We exemplify our methodology in Deep Reinforcement Learning (Deep RL). The performance of one execution of a Deep RL algorithm is a random variable. Therefore, several independent executions are needed to evaluate its performance. When comparing algorithms with random performance, a major question concerns the number of executions to perform to ensure that the result of the comparison is theoretically sound. Researchers in Deep RL often use less than 5 independent executions to compare algorithms: we claim that this is not enough in general. Moreover, when comparing more than 2 algorithms at once, we have to use a multiple tests procedure to preserve low error guarantees. We introduce AdaStop, a new statistical test based on multiple group sequential tests. When used to compare algorithms, AdaStop adapts the number of executions to stop as early as possible while ensuring that enough information has been collected to distinguish algorithms that have different score distributions. We prove theoretically that AdaStop has a low probability of making a (family-wise) error. We illustrate the effectiveness of AdaStop in various use-cases, including toy examples and Deep RL algorithms on challenging Mujoco environments. AdaStop is the first statistical test fitted to this sort of comparisons: it is both a significant contribution to statistics, and an important contribution to computational studies performed in reinforcement learning and in other domains.

cs.LG↗

arXiv2024

How to Shrink Confidence Sets for Many Equivalent Discrete Distributions?

We consider the situation when a learner faces a set of unknown discrete distributions $(p_k)_{k\in \mathcal K}$ defined over a common alphabet $\mathcal X$, and can build for each distribution $p_k$ an individual high-probability confidence set thanks to $n_k$ observations sampled from $p_k$. The set $(p_k)_{k\in \mathcal K}$ is structured: each distribution $p_k$ is obtained from the same common, but unknown, distribution q via applying an unknown permutation to $\mathcal X$. We call this \emph{permutation-equivalence}. The goal is to build refined confidence sets \emph{exploiting} this structural property. Like other popular notions of structure (Lipschitz smoothness, Linearity, etc.) permutation-equivalence naturally appears in machine learning problems, and to benefit from its potential gain calls for a specific approach. We present a strategy to effectively exploit permutation-equivalence, and provide a finite-time high-probability bound on the size of the refined confidence sets output by the strategy. Since a refinement is not possible for too few observations in general, under mild technical assumptions, our finite-time analysis establish when the number of observations $(n_k)_{k\in \mathcal K}$ are large enough so that the output confidence sets improve over initial individual sets. We carefully characterize this event and the corresponding improvement. Further, our result implies that the size of confidence sets shrink at asymptotic rates of $O(1/\sqrt{\sum_{k\in \mathcal K} n_k})$ and $O(1/\max_{k\in K} n_{k})$, respectively for elements inside and outside the support of q, when the size of each individual confidence set shrinks at respective rates of $O(1/\sqrt{n_k})$ and $O(1/n_k)$. We illustrate the practical benefit of exploiting permutation equivalence on a reinforcement learning task.

stat.ML↗

arXiv2024

Power Mean Estimation in Stochastic Monte-Carlo Tree_Search

Monte-Carlo Tree Search (MCTS) is a widely-used strategy for online planning that combines Monte-Carlo sampling with forward tree search. Its success relies on the Upper Confidence bound for Trees (UCT) algorithm, an extension of the UCB method for multi-arm bandits. However, the theoretical foundation of UCT is incomplete due to an error in the logarithmic bonus term for action selection, leading to the development of Fixed-Depth-MCTS with a polynomial exploration bonus to balance exploration and exploitation~\citep{shah2022journal}. Both UCT and Fixed-Depth-MCTS suffer from biased value estimation: the weighted sum underestimates the optimal value, while the maximum valuation overestimates it~\citep{coulom2006efficient}. The power mean estimator offers a balanced solution, lying between the average and maximum values. Power-UCT~\citep{dam2019generalized} incorporates this estimator for more accurate value estimates but its theoretical analysis remains incomplete. This paper introduces Stochastic-Power-UCT, an MCTS algorithm using the power mean estimator and tailored for stochastic MDPs. We analyze its polynomial convergence in estimating root node values and show that it shares the same convergence rate of $\mathcal{O}(n^{-1/2})$, with $n$ is the number of visited trajectories, as Fixed-Depth-MCTS, with the latter being a special case of the former. Our theoretical results are validated with empirical tests across various stochastic MDP environments.

cs.AI↗

arXiv2023

CRIMED: Lower and Upper Bounds on Regret for Bandits with Unbounded Stochastic Corruption

We investigate the regret-minimisation problem in a multi-armed bandit setting with arbitrary corruptions. Similar to the classical setup, the agent receives rewards generated independently from the distribution of the arm chosen at each time. However, these rewards are not directly observed. Instead, with a fixed $\varepsilon\in (0,\frac{1}{2})$, the agent observes a sample from the chosen arm's distribution with probability $1-\varepsilon$, or from an arbitrary corruption distribution with probability $\varepsilon$. Importantly, we impose no assumptions on these corruption distributions, which can be unbounded. In this setting, accommodating potentially unbounded corruptions, we establish a problem-dependent lower bound on regret for a given family of arm distributions. We introduce CRIMED, an asymptotically-optimal algorithm that achieves the exact lower bound on regret for bandits with Gaussian distributions with known variance. Additionally, we provide a finite-sample analysis of CRIMED's regret performance. Notably, CRIMED can effectively handle corruptions with $\varepsilon$ values as high as $\frac{1}{2}$. Furthermore, we develop a tight concentration result for medians in the presence of arbitrary corruptions, even with $\varepsilon$ values up to $\frac{1}{2}$, which may be of independent interest. We also discuss an extension of the algorithm for handling misspecification in Gaussian model.

stat.ML↗