Note:<\/strong> The proof of Theorem 8 is not correct. We do not know if the theorem holds true.)<\/p>\n","protected":false},"excerpt":{"rendered":"We study the stochastic multi-armed bandit problem when one knows the value \u00b5(\u22c6) of an optimal arm, as a well as a positive lower bound on the smallest positive gap \u2206. We propose a new randomized policy that attains a regret uniformly bounded over time in this setting. 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