Multi-Agent Lipschitz Bandits

Abstract

We study the decentralized multi-player stochastic bandit problem over a continuous, Lipschitz-structured action space where hard collisions yield zero reward. Our objective is to design a communication-free policy that maximizes collective reward, with coordination costs that are independent of the time horizon $T$. We propose a modular protocol that first solves the multi-agent coordination problem -- identifying and seating players on distinct high-value regions via a novel maxima-directed search -- and then decouples the problem into $N$ independent single-player Lipschitz bandits. We establish a near-optimal regret bound of $\tilde{O}(T^{(d+1)/(d+2)})$ plus a $T$-independent coordination cost, matching the single-player rate. To our knowledge, this is the first framework providing such guarantees, and it extends to general distance-threshold collision models.