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- W4327811002 abstract "We study linear contextual bandits in the misspecified setting, where the expected reward function can be approximated by a linear function class up to a bounded misspecification level $zeta>0$. We propose an algorithm based on a novel data selection scheme, which only selects the contextual vectors with large uncertainty for online regression. We show that, when the misspecification level $zeta$ is dominated by $tilde O (Delta / sqrt{d})$ with $Delta$ being the minimal sub-optimality gap and $d$ being the dimension of the contextual vectors, our algorithm enjoys the same gap-dependent regret bound $tilde O (d^2/Delta)$ as in the well-specified setting up to logarithmic factors. In addition, we show that an existing algorithm SupLinUCB (Chu et al., 2011) can also achieve a gap-dependent constant regret bound without the knowledge of sub-optimality gap $Delta$. Together with a lower bound adapted from Lattimore et al. (2020), our result suggests an interplay between misspecification level and the sub-optimality gap: (1) the linear contextual bandit model is efficiently learnable when $zeta leq tilde O(Delta / sqrt{d})$; and (2) it is not efficiently learnable when $zeta geq tilde Omega({Delta} / {sqrt{d}})$. Experiments on both synthetic and real-world datasets corroborate our theoretical results." @default.
- W4327811002 created "2023-03-19" @default.
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- W4327811002 date "2023-03-16" @default.
- W4327811002 modified "2023-09-29" @default.
- W4327811002 title "On the Interplay Between Misspecification and Sub-optimality Gap in Linear Contextual Bandits" @default.
- W4327811002 doi "https://doi.org/10.48550/arxiv.2303.09390" @default.
- W4327811002 hasPublicationYear "2023" @default.
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