Stochastically constrained best arm identification with Thompson sampling

We consider the problem of the best arm identification in the presence of stochastic constraints, where there is a finite number of arms associated with multiple performance measures . The goal is to identify the arm that optimizes the objective measure subject to constraints on the remaining measures. We will explore the popular idea of Thompson sampling (TS) as a means to solve it. To the best of our knowledge, it is the first attempt to extend TS to this problem. We will design a TS-based sampling algorithm, establish its asymptotic optimality in the rate of posterior convergence, and demonstrate its superior performance using numerical examples.