An Analysis of Ensemble Sampling

Chao Qin, Zheng Wen, Xiuyuan Lu, Benjamin Van Roy

Abstract: Ensemble sampling serves as a practical approximation to Thompson sampling when maintaining an exact posterior distribution over model parameters is computationally intractable. In this paper, we establish a Bayesian regret bound that ensures desirable behavior when ensemble sampling is applied to the linear bandit problem. This represents the first rigorous regret analysis of ensemble sampling and is made possible by leveraging information-theoretic concepts and novel analytic techniques that may prove useful beyond the scope of this paper.