Bypassing the Simulator: Near-Optimal Adversarial Linear Contextual Bandits

TL;DR

This paper introduces a computationally efficient algorithm for adversarial linear contextual bandits that achieves near-optimal regret without relying on simulators, improving upon previous methods in both regret bounds and practicality.

Contribution

It presents a novel approach that attains $ ilde{O}( oot{2}rom T)$ regret without simulators and handles misspecification, advancing the state-of-the-art in adversarial bandit algorithms.

Findings

Achieves $ ilde{O}( oot{2}rom T)$ regret without simulators

Provides a polynomial-time algorithm for sleeping bandits with adversarial loss

Handles linear loss with additive misspecification error effectively

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 $\widetilde{O}(T^{\frac{5}{6}})$, or are computationally inefficient. We greatly improve these results by achieving a regret of $\widetilde{O}(\sqrt{T})$ 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 Saha et al. [2020] 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.