Metalearning Linear Bandits by Prior Update

TL;DR

This paper studies how to improve Bayesian linear bandit algorithms by learning the prior across multiple tasks, showing that near-accurate priors lead to near-optimal performance and providing algorithms with regret guarantees.

Contribution

It introduces a meta-learning approach for updating priors in linear bandits, with theoretical regret bounds and empirical validation, addressing prior misspecification issues.

Findings

Performance remains close to the true prior when the estimated prior is sufficiently accurate.

The proposed algorithm achieves regret bounds comparable to those with known true prior.

Empirical results validate the theoretical guarantees and effectiveness of the method.

Abstract

Fully Bayesian approaches to sequential decision-making assume that problem parameters are generated from a known prior. In practice, such information is often lacking. This problem is exacerbated in setups with partial information, where a misspecified prior may lead to poor exploration and performance. In this work we prove, in the context of stochastic linear bandits and Gaussian priors, that as long as the prior is sufficiently close to the true prior, the performance of the applied algorithm is close to that of the algorithm that uses the true prior. Furthermore, we address the task of learning the prior through metalearning, where a learner updates her estimate of the prior across multiple task instances in order to improve performance on future tasks. We provide an algorithm and regret bounds, demonstrate its effectiveness in comparison to an algorithm that knows the correct prior, and support our theoretical results empirically. Our theoretical results hold for a broad class of algorithms, including Thompson Sampling and Information Directed Sampling.