Sequential Monte Carlo Bandits

Abstract

We extend Bayesian multi-armed bandit (MAB) algorithms beyond their original setting by making use of sequential Monte Carlo (SMC) methods. A MAB is a sequential decision making problem where the goal is to learn a policy that maximizes long term payoff, where only the reward of the executed action is observed. In the stochastic MAB, the reward for each action is generated from an unknown distribution, often assumed to be stationary. To decide which action to take next, a MAB agent must learn the characteristics of the unknown reward distribution, e.g., compute its sufficient statistics. However, closed-form expressions for these statistics are analytically intractable except for simple, stationary cases. We here utilize SMC for estimation of the statistics Bayesian MAB agents compute, and devise flexible policies that can address a rich class of bandit problems: i.e., MABs with nonlinear, stateless- and context-dependent reward distributions that evolve over time. We showcase how non-stationary bandits, where time dynamics are modeled via linear dynamical systems, can be successfully addressed by SMC-based Bayesian bandit agents. We empirically demonstrate good regret performance of the proposed SMC-based bandit policies in several MAB scenarios that have remained elusive, i.e., in non-stationary bandits with nonlinear rewards.