Cooperative and Stochastic Multi-Player Multi-Armed Bandit: Optimal Regret With Neither Communication Nor Collisions
Abstract
We consider the cooperative multi-player version of the stochastic multi-armed bandit problem. We study the regime where the players cannot communicate but have access to shared randomness. In prior work by the first two authors, a strategy for this regime was constructed for two players and three arms, with regret $\tilde{O}(\sqrt{T})$, and with no collisions at all between the players (with very high probability). In this paper we show that these properties (near-optimal regret and no collisions at all) are achievable for any number of players and arms. At a high level, the previous strategy heavily relied on a $2$-dimensional geometric intuition that was difficult to generalize in higher dimensions, while here we take a more combinatorial route to build the new strategy.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2020
- DOI:
- 10.48550/arXiv.2011.03896
- arXiv:
- arXiv:2011.03896
- Bibcode:
- 2020arXiv201103896B
- Keywords:
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- Computer Science - Machine Learning;
- Computer Science - Multiagent Systems;
- Statistics - Machine Learning