Computer Science > Computer Science and Game Theory
[Submitted on 26 Oct 2018 (v1), last revised 5 Apr 2021 (this version, v7)]
Title:Game of Thrones: Fully Distributed Learning for Multi-Player Bandits
View PDFAbstract:We consider an N-player multi-armed bandit game where each player chooses one out of M arms for T turns. Each player has different expected rewards for the arms, and the instantaneous rewards are independent and identically distributed or Markovian. When two or more players choose the same arm, they all receive zero reward. Performance is measured using the expected sum of regrets, compared with an optimal assignment of arms to players that maximizes the sum of expected rewards. We assume that each player only knows her actions and the reward she received each turn. Players cannot observe the actions of other players, and no communication between players is possible. We present a distributed algorithm and prove that it achieves an expected sum of regrets of near-O\left(\log T\right). This is the first algorithm to achieve a near order optimal regret in this fully distributed scenario. All other works have assumed that either all players have the same vector of expected rewards or that communication between players is possible.
Submission history
From: Ilai Bistritz [view email][v1] Fri, 26 Oct 2018 01:45:43 UTC (268 KB)
[v2] Mon, 29 Oct 2018 00:44:19 UTC (268 KB)
[v3] Thu, 7 Feb 2019 04:51:12 UTC (279 KB)
[v4] Mon, 28 Oct 2019 04:19:50 UTC (279 KB)
[v5] Mon, 13 Jan 2020 18:48:57 UTC (385 KB)
[v6] Tue, 3 Nov 2020 03:16:55 UTC (386 KB)
[v7] Mon, 5 Apr 2021 05:23:28 UTC (386 KB)
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