Mistake bounds on the noise-free multi-armed bandit game

Abstract We study the { 0 , 1 } -loss version of adaptive adversarial multi-armed bandit problems with α ( ≥ 1 ) lossless arms. For the problem, we show a tight bound K − α − Θ ( 1 / T ) on the minimax expected number of mistakes (1-losses), where K is the number of arms and T is the number of rounds.