Robust Multi-Agent Bandits Handle Heavy-Tailed Rewards.

The multi-armed bandit problem is a fundamental framework for sequential decision-making, typically studied under the assumption of sub-Gaussian (well-behaved) reward distributions. However, real-world applications often involve "heavy-tailed" rewards, meaning extreme outcomes are more likely, and interactions can be decentralized with agents having incomplete information. This research tackles these complexities in multi-agent multi-armed bandits.The study develops robust decentralized algorithms tailored for three specific scenarios of information asymmetry: agents with unobserved actions but common rewards, agents with observed actions but independent rewards, and agents with both unobserved actions and independent rewards. For each setting, the proposed algorithms come with regret guarantees that are nearly as good as those achieved by centralized systems dealing with heavy-tailed rewards. Experimental validation using Pareto-distributed rewards confirms the theoretical findings and illustrates the delicate balance required between synchronization, coordination, and exploration across these different information regimes.