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Creators/Authors contains: "Mridul Agarwal, Vaneet Aggarwal"

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  1. We consider the problem where N agents collaboratively interact with an instance of a stochastic K arm bandit problem for K N. The agents aim to simultaneously minimize the cumulative regret over all the agents for a total of T time steps, the number of communication rounds, and the number of bits in each communication round. We present Limited Communication Collaboration - Upper Confidence Bound (LCC-UCB), a doubling-epoch based algorithm where each agent communicates only after the end of the epoch and shares the index of the best arm it knows. With our algorithm, LCC-UCB, each agent enjoys a regret of O√(K/N + N)T, communicates for O(log T) steps and broadcasts O(log K) bits in each communication step. We extend the work to sparse graphs with maximum degree KG and diameter D to propose LCC-UCB-GRAPH which enjoys a regret bound of O√(D(K/N + KG)DT). Finally, we empirically show that the LCC-UCB and the LCC-UCB-GRAPH algorithms perform well and outperform strategies that communicate through a central node. 
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