Bandits with switching costs

Abstract

We study the adversarial multi-armed bandit problem in a setting where the player incurs a unit cost each time he switches actions. We prove that the player's T-round minimax regret in this setting is [EQUATION], thereby closing a fundamental gap in our understanding of learning with bandit feedback. In the corresponding full-information version of the problem, the minimax regret is known to grow at a much slower rate of Θ(√T). The difference between these two rates provides the first indication that learning with bandit feedback can be significantly harder than learning with full information feedback (previous results only showed a different dependence on the number of actions, but not on T.)

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