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Our goal is to identify the best arm with a minimal number of samplings under a given value of the error rate. We show the instance-specific sample complexity lower bounds for the problem. Then, we propose a context-aware version of the \"Track-and-Stop\" strategy, wherein the proportion of the arm draws tracks the set of optimal allocations and prove that the expected number of arm draws matches the lower bound asymptotically. We demonstrate that contextual information can be used to improve the efficiency of the identification of the best marginalized mean reward compared with the results of Garivier & Kaufmann (2016). 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