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I want to know if there are any references in the literature on multi-armed bandit problem where in one round, you can select $k > 1$ arms.

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Yes - Satyen Kale, Rob Schapire, and I have a recent paper (NIPS '10) on this very problem, where we consider choosing "slates" of arms instead of individual arms. We consider the cases when position matters in the slate and when it doesn't. We also analyze both the experts MAB "contextual" model and the expertless setting.

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    $\begingroup$ excellent ! always nice when the definitive expert answers :) $\endgroup$ Feb 25 '11 at 22:03

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