Top Feasible-Arm Subset Identification in Constrained Multi-Armed Bandit with Limited Budget

Abstract

We present an algorithm, "constrained successive accept or reject (CSAR)," for the problem of identifying the subset of top feasible-arms from a given finite set of arms with the limited sampling-budget equal to a given time-horizon when the sequential dynamics of the arms follows the model of a constrained multi-armed bandit. We provide a finite-time upper bound on the probability of the incorrect identification by CSAR that converges to zero with an exponential rate in the sampling-budget.