Adaptive Exploration in Linear Contextual Bandit

TL;DR

This paper introduces an adaptive algorithm for linear contextual bandits that achieves asymptotic optimality, good finite-time performance, and adapts to well-behaved context distributions, reducing regret significantly.

Contribution

The paper proposes a novel adaptive exploration algorithm for linear contextual bandits that combines asymptotic optimality with practical finite-time performance and automatic detection of favorable conditions.

Findings

Achieves asymptotic optimality in regret.

Performs well in finite-time experiments, outperforming baselines.

Automatically adapts to well-behaved context distributions, reducing regret.

Abstract

Contextual bandits serve as a fundamental model for many sequential decision making tasks. The most popular theoretically justified approaches are based on the optimism principle. While these algorithms can be practical, they are known to be suboptimal asymptotically. On the other hand, existing asymptotically optimal algorithms for this problem do not exploit the linear structure in an optimal way and suffer from lower-order terms that dominate the regret in all practically interesting regimes. We start to bridge the gap by designing an algorithm that is asymptotically optimal and has good finite-time empirical performance. At the same time, we make connections to the recent literature on when exploration-free methods are effective. Indeed, if the distribution of contexts is well behaved, then our algorithm acts mostly greedily and enjoys sub-logarithmic regret. Furthermore, our approach is adaptive in the sense that it automatically detects the nice case. Numerical results demonstrate significant regret reductions by our method relative to several baselines.