We study the power of different types of adaptive (nonoblivious) adversaries in the setting of prediction with expert advice, under both full-information and bandit feedback. We measure the player\u2019s performance using a new notion of regret, also known as policy regret, which better captures the adversary\u2019s adaptiveness to the player\u2019s behavior. In a setting where losses are allowed to drift, we characterize \u2014in a nearly complete manner\u2014 the power of adaptive adversaries with bounded memories and switching costs. In particular, we show that with switching costs, the attainable rate with bandit feedback is \u0398( e T 2\/3 ). Interestingly, this rate is significantly worse than the \u0398(\u221a T) rate attainable with switching costs in the full-information case. Via a novel reduction from experts to bandits, we also show that a bounded memory adversary can force \u0398( e T 2\/3 ) regret even in the full information case, proving that switching costs are easier to control than bounded memory adversaries. Our lower bounds rely on a new stochastic adversary strategy that generates loss processes with strong dependencies.<\/p>\n","protected":false},"excerpt":{"rendered":"
We study the power of different types of adaptive (nonoblivious) adversaries in the setting of prediction with expert advice, under both full-information and bandit feedback. We measure the player\u2019s performance using a new notion of regret, also known as policy regret, which better captures the adversary\u2019s adaptiveness to the player\u2019s behavior. 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