Piecewise Stationary Bandits under Risk Criteria

Piecewise stationary stochastic multi-armed bandits have been extensively explored in the risk-neutral and sub-Gaussian setting. In this work, we consider a multi-armed bandit framework in which the reward distributions are heavy-tailed and non-stationary, and evaluate the performance of algorithms using general risk criteria. Specifically, we make the following contributions: (i) We first propose a non-parametric change detection algorithm that can detect general distributional changes in heavy-tailed distributions. (ii) We then propose a truncation-based UCB-type bandit algorithm integrating the above regime change detection algorithm to minimize the regret of the non-stationary learning problem. (iii) Finally, we establish the regret bounds for the proposed bandit algorithm by characterizing the statistical properties of the general change detection algorithm, along with a novel regret analysis.