Coordinating Unknown Lipschitz Constants in Multiplayer Bandits

A new arXiv paper (2608.10526) addresses cooperative multi-agent bandits in continuous action spaces where the Lipschitz constant is unknown. The study, motivated by decentralized applications, examines three information structures: unobserved actions with common rewards, observed actions with independent rewards, and unobserved actions with independent rewards. For each, the authors design an algorithm that estimates the Lipschitz constant, discretizes the joint action space, and applies a cooperative bandit method. A key challenge is that players must agree on the same discretization without communication after learning begins. The paper proves regret guarantees showing that common rewards and observable actions provide agreement for free, while in their absence, agreement can be achieved through dithered quantization at no cost in the regret bound. The work contributes to the theoretical understanding of multi-agent decision-making under uncertainty.