Information Complexity in Bandit Subset Selection

author: Emilie Kaufmann, Telecom ParisTech
published: Aug. 9, 2013,   recorded: June 2013,   views: 2861


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We consider the problem of efficiently exploring the arms of a stochastic bandit to identify the best subset. Under the PAC and the fixed-budget formulations, we derive improved bounds by using KL-divergence-based confidence intervals. Whereas the application of a similar idea in the regret setting has yielded bounds in terms of the KL-divergence between the arms, our bounds in the pure-exploration setting involve the Chernoff information between the arms. In addition to introducing this novel quantity to the bandits literature, we contribute a comparison between the “racing” and “smart sampling” strategies for pure-exploration problems, finding strong evidence in favor of the latter.

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