Pessimism for Offline Linear Contextual Bandits using $\ell_p$ Confidence SetsDownload PDF

Published: 31 Oct 2022, Last Modified: 08 Jan 2023NeurIPS 2022 AcceptReaders: Everyone
Keywords: offline reinforcement learning, pessimism, linear contextual bandits
TL;DR: A new estimator for offline linear contextual bandits
Abstract: We present a family $\{\widehat{\pi}_p\}_{p\ge 1}$ of pessimistic learning rules for offline learning of linear contextual bandits, relying on confidence sets with respect to different $\ell_p$ norms, where $\widehat{\pi}_2$ corresponds to Bellman-consistent pessimism (BCP), while $\widehat{\pi}_\infty$ is a novel generalization of lower confidence bound (LCB) to the linear setting. We show that the novel $\widehat{\pi}_\infty$ 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 $\widehat{\pi}_2$.
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