Optimal Thompson Sampling strategies for support-aware CVaR bandits

Dorian Baudry (1, 2) , Romain Gautron (3, 4) , Emilie Kaufmann (1, 2) , Odalric-Ambrym Maillard (2)

1 CNRS - Centre National de la Recherche Scientifique
2 Scool - Scool
3 UPR AIDA - Agroécologie et Intensification Durables des cultures annuelles
4 Cirad-PERSYST - Département Performances des systèmes de production et de transformation tropicaux

In this paper we study a multi-arm bandit problem in which the quality of each arm is measured by the Conditional Value at Risk (CVaR) at some level alpha of the reward distribution. While existing works in this setting mainly focus on Upper Confidence Bound algorithms, we introduce a new Thompson Sampling approach for CVaR bandits on bounded rewards that is flexible enough to solve a variety of problems grounded on physical resources. Building on a recent work by Riou & Honda (2020), we introduce B-CVTS for continuous bounded rewards and M-CVTS for multinomial distributions. On the theoretical side, we provide a non-trivial extension of their analysis that enables to theoretically bound their CVaR regret minimization performance. Strikingly, our results show that these strategies are the first to provably achieve asymptotic optimality in CVaR bandits, matching the corresponding asymptotic lower bounds for this setting. Further, we illustrate empirically the benefit of Thompson Sampling approaches both in a realistic environment simulating a use-case in agriculture and on various synthetic examples.

Domaines: Informatique [cs]; Machine Learning [stat.ML]

Dorian Baudry, Romain Gautron, Emilie Kaufmann, Odalric-Ambrym Maillard. Optimal Thompson Sampling strategies for support-aware CVaR bandits. 38th International Conference on Machine Learning, Jul 2021, Virtual, United States. ⟨hal-03447244⟩