# Nearly Minimax-Optimal Regret for Linearly Parameterized Bandits

@article{Li2019NearlyMR, title={Nearly Minimax-Optimal Regret for Linearly Parameterized Bandits}, author={Yingkai Li and Yining Wang and Yuanshuo Zhou}, journal={ArXiv}, year={2019}, volume={abs/1904.00242} }

We study the linear contextual bandit problem with finite action sets. When the problem dimension is $d$, the time horizon is $T$, and there are $n \leq 2^{d/2}$ candidate actions per time period, we (1) show that the minimax expected regret is $\Omega(\sqrt{dT (\log T) (\log n)})$ for every algorithm, and (2) introduce a Variable-Confidence-Level (VCL) SupLinUCB algorithm whose regret matches the lower bound up to iterated logarithmic factors. Our algorithmic result saves two $\sqrt{\log T…

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