Constrained Best Arm Identification in Grouped Bandits

Abstract

We study a grouped bandit setting where each arm comprises multiple independent sub-arms referred to as attributes. Each attribute of each arm has an independent stochastic reward. We impose the constraint that for an arm to be deemed feasible, the mean reward of all its attributes must exceed a specified threshold. The goal is to identify the arm with the highest mean reward averaged across attributes among the set of feasible arms in the fixed confidence setting. We first characterize a fundamental limit on the performance of any policy. Following this, we propose a near-optimal confidence interval-based policy to solve this problem and provide analytical guarantees. We compare the performance of the proposed policy with suitably modified versions of action elimination algorithms through simulations.