Bypassing the Simulator: Near-Optimal Adversarial Linear Contextual Bandits

Published: 21 Sept 2023, Last Modified: 02 Nov 2023NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: adversarial linear contextual bandits, log-determinant barrier
Abstract: We consider the adversarial linear contextual bandit problem, where the loss vectors are selected fully adversarially and the per-round action set (i.e. the context) is drawn from a fixed distribution. Existing methods for this problem either require access to a simulator to generate free i.i.d. contexts, achieve a sub-optimal regret no better than $\tilde{\mathcal{O}}(T^{\frac{5}{6}})$, or are computationally inefficient. We greatly improve these results by achieving a regret of $\tilde{\mathcal{O}}(\sqrt{T})$ without a simulator, while maintaining computational efficiency when the action set in each round is small. In the special case of sleeping bandits with adversarial loss and stochastic arm availability, our result answers affirmatively the open question by [SGV20] on whether there exists a polynomial-time algorithm with $poly(d)\sqrt{T}$ regret. Our approach naturally handles the case where the loss is linear up to an additive misspecification error, and our regret shows near-optimal dependence on the magnitude of the error.
Supplementary Material: pdf
Submission Number: 4987