Robust Multi-Agent Bandits with Heavy-Tailed Rewards and Information Asymmetry

The multi-armed bandit problem is a central framework in sequential decision-making, extensively studied under sub-Gaussian reward assumptions. However, real-world applications often involve heavy-tailed reward distributions and decentralized, information-asymmetric interactions. We study multi-agent multi-armed bandits with heavy-tailed rewards under three information-asymmetry regimes: unobserved actions with common rewards, observed actions with independent rewards, and unobserved actions with independent rewards. We develop robust decentralized algorithms for each setting and derive regret guarantees that nearly match centralized heavy-tailed rates. Experiments on a Pareto-distributed reward environment validate our theoretical findings and illustrate the trade-offs between synchronization, coordination, and exploration across the three regimes.

Coordinating the Unknown Lipschitz Constant in Multiplayer Bandits

Motivated by decentralized applications, we study cooperative multi-agent bandits in continuous (Lipschitz) action spaces when the Lipschitz constant is unknown. We consider three information structures: (A)~unobserved actions with common rewards, (B)~observed actions with independent rewards, and (C)~unobserved actions with independent rewards. In each case we design and analyze an algorithm that estimates the Lipschitz constant, chooses a discretization of the joint action space, and applies a cooperative bandit method to the induced discrete problem. Players never communicate once learning starts, so the central difficulty is that they must reach the \emph{same} discretization from their own data. We prove regret guarantees showing that common rewards and observable actions each supply this agreement for free, and that in their absence agreement can still be bought, through a dithered quantization of the estimate, at no cost in the leading order of the regret.