Constrained Contextual Bandits with Adversarial Contexts

TL;DR

This paper introduces a new framework for budget-constrained contextual bandits with adversarial contexts, improving guarantees and efficiency over prior stochastic-focused methods.

Contribution

It proposes a modular reduction approach leveraging online regression oracles to handle adversarial contexts in budget-constrained bandits.

Findings

Achieves improved guarantees for adversarial contexts.

Provides an efficient algorithm with transparent analysis.

Extends the $ extsf{SquareCB}$ framework to adversarial settings.

Abstract

We study budget-constrained contextual bandits with adversarial contexts, where each action yields a random reward and incurs a random cost. We adopt the standard realizability assumption: conditioned on the observed context, rewards and costs are drawn independently from fixed distributions whose expectations belong to known function classes. We focus on the continuing setting, in which the algorithm operates over the entire horizon even after the budget for cumulative cost is exhausted. In this setting, the objective is to simultaneously control regret and the violation of the budget constraint. Building on the seminal $\mathsf{SquareCB}$ framework of Foster et al. [2018], we propose a simple and modular framework that leverages online regression oracles to reduce the constrained problem to a standard unconstrained contextual bandit problem with adaptively defined surrogate reward functions. In contrast to prior works, which focus on stochastic contexts, our reduction yields improved guarantees for more general adversarial contexts, together with an efficient algorithm with a compact and transparent analysis.