Pure Exploration under Mediators’ Feedback

Published: 27 Oct 2023, Last Modified: 22 Dec 2023RealML-2023EveryoneRevisionsBibTeX
Keywords: Pure Exploration, Stochastic Bandits
TL;DR: We study the variant of Best-arm identification problems, where there the agent has partial or no control over the arms being pulled at each round.
Abstract: Stochastic multi-armed bandits are a sequential-decision-making framework, where, at each interaction step, the learner selects an arm and observes a stochastic reward. Within the context of best-arm identification (BAI) problems, the goal of the agent lies in finding the optimal arm, i.e., the one with the highest expected reward, as accurately and efficiently as possible. Nevertheless, the sequential interaction protocol of classical BAI problems, where the agent has complete control over the arm being pulled at each round, does not effectively model several decision-making problems of interest (e.g., off-policy learning, human feedback). For this reason, in this work, we propose a novel strict generalization of the classical BAI problem that we refer to as best-arm identification under mediators’ feedback (BAI-MF). More specifically, we consider the scenario in which the learner has access to a set of mediators, each of which selects the arms on the agent’s behalf according to a stochastic and possibly unknown policy. The mediator, then, communicates back to the agent the pulled arm together with the observed reward. In this setting, the agent’s goal lies in sequentially choosing which mediator to query to identify with high probability the optimal arm while minimizing the identification time, i.e., the sample complexity. To this end, we first derive and analyze a statistical lower bound on the sample complexity specific to our general mediator feedback scenario. Then, we propose a sequential decision-making strategy for discovering the best arm; as our theory verifies, this algorithm matches the lower bound both almost surely and in expectation.
Submission Number: 11