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arXiv · 1110.4322

An Optimal Algorithm for Linear Bandits

Nicolò Cesa-Bianchi·Sham Kakade
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Abstract

We provide the first algorithm for online bandit linear optimization whose regret after T rounds is of order sqrt{Td ln N} on any finite class X of N actions in d dimensions, and of order d*sqrt{T} (up to log factors) when X is infinite. These bounds are not improvable in general. The basic idea utilizes tools from convex geometry to construct what is essentially an optimal exploration basis. We also present an application to a model of linear bandits with expert advice. Interestingly, these results show that bandit linear optimization with expert advice in d dimensions is no more difficult (in terms of the achievable regret) than the online d-armed bandit problem with expert advice (where EXP4 is optimal).

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Nicolò Cesa-Bianchi, Sham Kakade. 2012-02-14. An Optimal Algorithm for Linear Bandits. https://arxiv.org/abs/1110.4322

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