A Risk-Averse Framework for Non-Stationary Stochastic Multi-Armed Bandits

In a typical stochastic multi-armed bandit problem, the objective is often to maximize the expected sum of rewards over some time horizon $T$. While the choice of a strategy that accomplishes that is optimal with no additional information, it is no longer the case when provided additional environment-specific knowledge. In particular, in areas of high volatility like healthcare or finance, a naive reward maximization approach often does not accurately capture the complexity of the learning problem and results in unreliable solutions. To tackle problems of this nature, we propose a framework of adaptive risk-aware strategies that operate in non-stationary environments. Our framework incorporates various risk measures prevalent in the literature to map multiple families of multi-armed bandit algorithms into a risk-sensitive setting. In addition, we equip the resulting algorithms with the Restarted Bayesian Online Change-Point Detection (R-BOCPD) algorithm and impose a (tunable) forced exploration strategy to detect local (per-arm) switches. We provide finite-time theoretical guarantees and an asymptotic regret bound of order $\tilde O(\sqrt{K_T T})$ up to time horizon $T$ with $K_T$ the total number of change-points. In practice, our framework compares favorably to the state-of-the-art in both synthetic and real-world environments and manages to perform efficiently with respect to both risk-sensitivity and non-stationarity

Deep Reinforcement Learning Algorithms for Hybrid V2X Communication: A Benchmarking Study

In today's era, autonomous vehicles demand a safety level on par with aircraft. Taking a cue from the aerospace industry, which relies on redundancy to achieve high reliability, the automotive sector can also leverage this concept by building redundancy in V2X (Vehicle-to-Everything) technologies. Given the current lack of reliable V2X technologies, this idea is particularly promising. By deploying multiple RATs (Radio Access Technologies) in parallel, the ongoing debate over the standard technology for future vehicles can be put to rest. However, coordinating multiple communication technologies is a complex task due to dynamic, time-varying channels and varying traffic conditions. This paper addresses the vertical handover problem in V2X using Deep Reinforcement Learning (DRL) algorithms. The goal is to assist vehicles in selecting the most appropriate V2X technology (DSRC/V-VLC) in a serpentine environment. The results show that the benchmarked algorithms outperform the current state-of-the-art approaches in terms of redundancy and usage rate of V-VLC headlights. This result is a significant reduction in communication costs while maintaining a high level of reliability. These results provide strong evidence for integrating advanced DRL decision mechanisms into the architecture as a promising approach to solving the vertical handover problem in V2X

Contribution à des problèmes statistiques d'ordonnancement et d'apprentissage par renforcement avec aversion au risque

Les travaux de cette thèse se situent à l’interface de deux thématiques de l'apprentissage automatique : l’apprentissage de préférences d'une part, et l’apprentissage par renforcement de l'autre. La première consiste à percoler différents classements d’un même ensemble d’objets afin d’en extraire un ordre général, la seconde à identifier séquentiellement une stratégie optimale en observant des récompenses sanctionnant chaque action essayée. La structure de la thèse suit ce découpage thématique. En première partie, le paradigme de minimisation du risque empirique est utilisé à des fins d'ordonnancement. Partant du problème d’apprentissage supervisé de règles d’ordonnancement à partir de données étiquetées de façon binaire, une extension est proposée au cas où les étiquettes prennent des valeurs continues. Les critères de performance usuels dans le cas binaire, à savoir la courbe caractéristique de l’opérateur de réception (COR) et l’aire sous la courbe COR (ASC), sont étendus au cas continu : les métriques COR intégrée (CORI) et ASC intégrée (ASCI) sont introduites à cet effet. Le second problème d'ordonnancement étudié est celui de l'agrégation de classements à travers l'identification du consensus de Kemeny. En particulier, une relaxation au problème plus général de la réduction de la dimensionnalité dans l'espace des distributions sur le groupe symétrique est formulée à l'aide d'outils mathématiques empruntés à la théorie du transport optimal. La seconde partie de cette thèse s'intéresse à l'apprentissage par renforcement. Des problèmes de bandit manchot sont analysés dans des contextes où la performance moyenne n'est pas pertinente et où la gestion du risque prévaut. Enfin, le problème plus général de l'apprentissage par renforcement distributionnel, dans lequel le décideur cherche à connaître l'entière distribution de sa performance et non pas uniquement sa valeur moyenne, est considéré. De nouveaux opérateurs de programmation dynamique ainsi que leurs pendants atomiques mènent à de nouveaux algorithmes stochastiques distributionnels.This thesis divides into two parts: the first part is on ranking and the second on risk-aware reinforcement learning. While binary classification is the flagship application of empirical risk minimization (ERM), the main paradigm of machine learning, more challenging problems such as bipartite ranking can also be expressed through that setup. In bipartite ranking, the goal is to order, by means of scoring methods, all the elements of some feature space based on a training dataset composed of feature vectors with their binary labels. This thesis extends this setting to the continuous ranking problem, a variant where the labels are taking continuous values instead of being simply binary. The analysis of ranking data, initiated in the 18th century in the context of elections, has led to another ranking problem using ERM, namely ranking aggregation and more precisely the Kemeny's consensus approach. From a training dataset made of ranking data, such as permutations or pairwise comparisons, the goal is to find the single "median permutation" that best corresponds to a consensus order. We present a less drastic dimensionality reduction approach where a distribution on rankings is approximated by a simpler distribution, which is not necessarily reduced to a Dirac mass as in ranking aggregation.For that purpose, we rely on mathematical tools from the theory of optimal transport such as Wasserstein metrics. The second part of this thesis focuses on risk-aware versions of the stochastic multi-armed bandit problem and of reinforcement learning (RL), where an agent is interacting with a dynamic environment by taking actions and receiving rewards, the objective being to maximize the total payoff. In particular, a novel atomic distributional RL approach is provided: the distribution of the total payoff is approximated by particles that correspond to trimmed means

Ranking and risk-aware reinforcement learning

This thesis divides into two parts: the first part is on ranking and the second on risk-aware reinforcement learning. While binary classification is the flagship application of empirical risk minimization (ERM), the main paradigm of machine learning, more challenging problems such as bipartite ranking can also be expressed through that setup. In bipartite ranking, the goal is to order, by means of scoring methods, all the elements of some feature space based on a training dataset composed of feature vectors with their binary labels. This thesis extends this setting to the continuous ranking problem, a variant where the labels are taking continuous values instead of being simply binary. The analysis of ranking data, initiated in the 18th century in the context of elections, has led to another ranking problem using ERM, namely ranking aggregation and more precisely the Kemeny's consensus approach. From a training dataset made of ranking data, such as permutations or pairwise comparisons, the goal is to find the single "median permutation" that best corresponds to a consensus order. We present a less drastic dimensionality reduction approach where a distribution on rankings is approximated by a simpler distribution, which is not necessarily reduced to a Dirac mass as in ranking aggregation.For that purpose, we rely on mathematical tools from the theory of optimal transport such as Wasserstein metrics. The second part of this thesis focuses on risk-aware versions of the stochastic multi-armed bandit problem and of reinforcement learning (RL), where an agent is interacting with a dynamic environment by taking actions and receiving rewards, the objective being to maximize the total payoff. In particular, a novel atomic distributional RL approach is provided: the distribution of the total payoff is approximated by particles that correspond to trimmed means.Les travaux de cette thèse se situent à l’interface de deux thématiques de l'apprentissage automatique : l’apprentissage de préférences d'une part, et l’apprentissage par renforcement de l'autre. La première consiste à percoler différents classements d’un même ensemble d’objets afin d’en extraire un ordre général, la seconde à identifier séquentiellement une stratégie optimale en observant des récompenses sanctionnant chaque action essayée. La structure de la thèse suit ce découpage thématique. En première partie, le paradigme de minimisation du risque empirique est utilisé à des fins d'ordonnancement. Partant du problème d’apprentissage supervisé de règles d’ordonnancement à partir de données étiquetées de façon binaire, une extension est proposée au cas où les étiquettes prennent des valeurs continues. Les critères de performance usuels dans le cas binaire, à savoir la courbe caractéristique de l’opérateur de réception (COR) et l’aire sous la courbe COR (ASC), sont étendus au cas continu : les métriques COR intégrée (CORI) et ASC intégrée (ASCI) sont introduites à cet effet. Le second problème d'ordonnancement étudié est celui de l'agrégation de classements à travers l'identification du consensus de Kemeny. En particulier, une relaxation au problème plus général de la réduction de la dimensionnalité dans l'espace des distributions sur le groupe symétrique est formulée à l'aide d'outils mathématiques empruntés à la théorie du transport optimal. La seconde partie de cette thèse s'intéresse à l'apprentissage par renforcement. Des problèmes de bandit manchot sont analysés dans des contextes où la performance moyenne n'est pas pertinente et où la gestion du risque prévaut. Enfin, le problème plus général de l'apprentissage par renforcement distributionnel, dans lequel le décideur cherche à connaître l'entière distribution de sa performance et non pas uniquement sa valeur moyenne, est considéré. De nouveaux opérateurs de programmation dynamique ainsi que leurs pendants atomiques mènent à de nouveaux algorithmes stochastiques distributionnels

Continuous Ranking trough Oriented Recursive Partitions

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Profitable Bandits

International audienceOriginally motivated by default risk management applications, this paper investigates a novel problem, referred to as the profitable bandit problem here. At each step, an agent chooses a subset of the K ≥ 1 possible actions. For each action chosen, she then respectively pays and receives the sum of a random number of costs and rewards. Her objective is to maximize her cumulated profit. We adapt and study three well-known strategies in this purpose, that were proved to be most efficient in other settings: kl-UCB, Bayes-UCB and Thompson Sampling. For each of them, we prove a finite time regret bound which, together with a lower bound we obtain as well, establishes asymptotic optimality in some cases. Our goal is also to compare these three strategies from a theoretical and empirical perspective both at the same time. We give simple, self-contained proofs that emphasize their similarities, as well as their differences. While both Bayesian strategies are automatically adapted to the geometry of information, the numerical experiments carried out show a slight advantage for Thompson Sampling in practice

Dimensionality Reduction and (Bucket) Ranking: a Mass Transportation Approach.

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