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2004

Nearly Tight Bounds for the Continuum-Armed Bandit Problem

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Nearly Tight Bounds for the Continuum-Armed Bandit Problem
In the multi-armed bandit problem, an online algorithm must choose from a set of strategies in a sequence of n trials so as to minimize the total cost of the chosen strategies. While nearly tight upper and lower bounds are known in the case when the strategy set is finite, much less is known when there is an infinite strategy set. Here we consider the case when the set of strategies is a subset of Rd , and the cost functions are continuous. In the d = 1 case, we improve on the best-known upper and lower bounds, closing the gap to a sublogarithmic factor. We also consider the case where d > 1 and the cost functions are convex, adapting a recent online convex optimization algorithm of Zinkevich to the sparser feedback model of the multi-armed bandit problem.
Robert D. Kleinberg
Added 31 Oct 2010
Updated 31 Oct 2010
Type Conference
Year 2004
Where NIPS
Authors Robert D. Kleinberg
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