Game of Thrones: Fully Distributed Learning for Multi-Player Bandits
We consider a multi-armed bandit game where N players compete for 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 to optimal assignment of arms to players. 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( T). 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.
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