Optimal Fair Multi-Agent Bandits
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In this paper, we study the problem of fair multi-agent multi-arm bandit learning when agents do not communicate with each other, except collision information, provided to agents accessing the same arm simultaneously. We provide an algorithm with regret O(N^3 log N log T ) (assuming bounded rewards, with unknown bound). This significantly improves previous results which had regret of order O(log T loglog T) and exponential dependence on the number of agents. The result is attained by using a distributed auction algorithm to learn the sample-optimal matching, a new type of exploitation phase whose length is derived from the observed samples, and a novel order-statistics-based regret analysis. Simulation results present the dependence of the regret on log T.
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