An Optimal Algorithm for Linear Bandits
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).
Cite
@article{arxiv.1110.4322,
title = {An Optimal Algorithm for Linear Bandits},
author = {Nicolò Cesa-Bianchi and Sham Kakade},
journal= {arXiv preprint arXiv:1110.4322},
year = {2012}
}
Comments
This paper is superseded by S. Bubeck, N. Cesa-Bianchi, and S.M. Kakade, "Towards minimax policies for online linear optimization with bandit feedback"