Near-Optimal Collaborative Learning in Bandits
This work addresses the challenge of efficient collaboration in bandit settings for agents needing personalized decisions, extending models like federated learning with personalization, but it is incremental as it builds on existing frameworks.
The paper tackles the problem of collaborative multi-agent bandit learning where agents must identify or play optimal arms based on mixed rewards, requiring communication. It provides new lower bounds for sample complexity and regret, and proposes a near-optimal algorithm for pure exploration based on phased elimination with a data-dependent sampling scheme.
This paper introduces a general multi-agent bandit model in which each agent is facing a finite set of arms and may communicate with other agents through a central controller in order to identify, in pure exploration, or play, in regret minimization, its optimal arm. The twist is that the optimal arm for each agent is the arm with largest expected mixed reward, where the mixed reward of an arm is a weighted sum of the rewards of this arm for all agents. This makes communication between agents often necessary. This general setting allows to recover and extend several recent models for collaborative bandit learning, including the recently proposed federated learning with personalization (Shi et al., 2021). In this paper, we provide new lower bounds on the sample complexity of pure exploration and on the regret. We then propose a near-optimal algorithm for pure exploration. This algorithm is based on phased elimination with two novel ingredients: a data-dependent sampling scheme within each phase, aimed at matching a relaxation of the lower bound.