Related papers: Adversarial Contextual Bandits Go Kernelized

Adversarial Contextual Bandits Go Kernelized

URL: http://arxiv.org/abs/2310.01609v1
Date: Mon, 2 Oct 2023 19:59:39 GMT
Title: Adversarial Contextual Bandits Go Kernelized
Authors: Gergely Neu, Julia Olkhovskaya, Sattar Vakili
Abstract summary: We study a generalization of the problem of online learning in adversarial linear contextual bandits by incorporating loss functions that belong to a Hilbert kernel space. We propose a new optimistically biased estimator for the loss functions and reproducing near-optimal regret guarantees.
Score: 21.007410990554522
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
Abstract: We study a generalization of the problem of online learning in adversarial linear contextual bandits by incorporating loss functions that belong to a reproducing kernel Hilbert space, which allows for a more flexible modeling of complex decision-making scenarios. We propose a computationally efficient algorithm that makes use of a new optimistically biased estimator for the loss functions and achieves near-optimal regret guarantees under a variety of eigenvalue decay assumptions made on the underlying kernel. Specifically, under the assumption of polynomial eigendecay with exponent $c>1$, the regret is $\widetilde{O}(KT^{\frac{1}{2}(1+\frac{1}{c})})$, where $T$ denotes the number of rounds and $K$ the number of actions. Furthermore, when the eigendecay follows an exponential pattern, we achieve an even tighter regret bound of $\widetilde{O}(\sqrt{T})$. These rates match the lower bounds in all special cases where lower bounds are known at all, and match the best known upper bounds available for the more well-studied stochastic counterpart of our problem.

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