Pessimism for Offline Linear Contextual Bandits using $\ell_p$ Confidence Sets

Gene Li; Cong Ma; Nathan Srebro

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arXiv · 2205.10671

Pessimism for Offline Linear Contextual Bandits using $\ell_p$ Confidence Sets

Gene Li·Cong Ma·Nathan Srebro

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Abstract

We present a family $\{\hat{\pi}\}_{p\ge 1}$ of pessimistic learning rules for offline learning of linear contextual bandits, relying on confidence sets with respect to different $\ell_p$ norms, where $\hat{\pi}_2$ corresponds to Bellman-consistent pessimism (BCP), while $\hat{\pi}_\infty$ is a novel generalization of lower confidence bound (LCB) to the linear setting. We show that the novel $\hat{\pi}_\infty$ learning rule is, in a sense, adaptively optimal, as it achieves the minimax performance (up to log factors) against all $\ell_q$-constrained problems, and as such it strictly dominates all other predictors in the family, including $\hat{\pi}_2$.

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Gene Li, Cong Ma, Nathan Srebro. 2022-05-21. Pessimism for Offline Linear Contextual Bandits using $\ell_p$ Confidence Sets. https://arxiv.org/abs/2205.10671

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