Title: Enhancing Adversarial Linear Contextual Bandits Through Reduction

Abstract: We introduce a near-optimal, oracle-efficient algorithm for linear contextual bandits characterized by adversarial losses and stochastic action sets. This method relies exclusively on a linear optimization oracle to handle action sets at each step. By reducing the problem to adversarial linear bandits with fixed action sets that are robust to misspecification, we achieve a regret bound of $\widetilde{\mathcal{O}}(\min{d^2\sqrt{T}, \sqrt{d^3T\log K}})$ without needing to know the context distribution or having access to a context simulator. Here, $d$ represents the feature dimension, $K$ denotes an upper bound on the number of actions per round, and $T$ is the total number of rounds. The algorithm operates in $\mathrm{poly}(d,T)$ time and requires $\mathrm{poly}(d,T)$ invocations of the linear optimization oracles.

This work addresses an open problem posed by Liu et al. (2023), demonstrating that $\mathrm{poly}(d)\sqrt{T}$ regret can be attained in polynomial time regardless of the number of actions. Specifically, for combinatorial bandits featuring adversarial losses and stochastic action sets, our approach is the first to deliver $\mathrm{poly}(d)\sqrt{T}$ regret within polynomial time; notably, to our knowledge, no previous algorithm has achieved even $o(T)$ regret in polynomial time for this setting. Furthermore, if a simulator is available, the regret bound improves to $\widetilde{\mathcal{O}}(d\sqrt{L^\star})$, where $L^\star$ signifies the cumulative loss incurred by the optimal policy.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC