Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oracles

TL;DR

This paper introduces a universal, optimal reduction from contextual bandits to online regression, enabling efficient algorithms with theoretical guarantees for a wide range of function classes, including nonparametric and adversarial contexts.

Contribution

It provides the first universal, minimax optimal reduction from contextual bandits to online regression with no overhead, applicable to general, possibly nonparametric, and adversarial settings.

Findings

Achieves minimax optimal rates for contextual bandits with general function classes.

Requires no distributional assumptions beyond realizability.

Works efficiently even with adversarially chosen contexts.

Abstract

A fundamental challenge in contextual bandits is to develop flexible, general-purpose algorithms with computational requirements no worse than classical supervised learning tasks such as classification and regression. Algorithms based on regression have shown promising empirical success, but theoretical guarantees have remained elusive except in special cases. We provide the first universal and optimal reduction from contextual bandits to online regression. We show how to transform any oracle for online regression with a given value function class into an algorithm for contextual bandits with the induced policy class, with no overhead in runtime or memory requirements. We characterize the minimax rates for contextual bandits with general, potentially nonparametric function classes, and show that our algorithm is minimax optimal whenever the oracle obtains the optimal rate for regression. Compared to previous results, our algorithm requires no distributional assumptions beyond realizability, and works even when contexts are chosen adversarially.