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We consider a variant of the traditional multi-armed bandit problem in whicheach arm is only able to provide one-bit feedback during each pull based on itspast history of rewards. Our main result is the following: given an upperconfidence bound policy which uses full-reward feedback, there exists a codingscheme for generating one-bit feedback, and a corresponding decoding scheme andarm selection policy, such that the ratio of the regret achieved by our policyand the regret of the full-reward feedback policy asymptotically approachesone.

One-bit feedback is sufficient for upper confidence bound policies