Metalearning Linear Bandits by Prior Update

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.

References in corpus (10)

• Thompson Sampling for Contextual Bandits with Linear Payoffs
• A PAC-Bayesian bound for Lifelong Learning
• Meta-Learning by Adjusting Priors Based on Extended PAC-Bayes Theory
• Optimality of Thompson Sampling for Gaussian Bandits Depends on Priors
• Meta-learning of Sequential Strategies
• Are sample means in multi-armed bandits positively or negatively biased?
• An Information-Theoretic Analysis for Thompson Sampling with Many Actions
• Meta Dynamic Pricing: Transfer Learning Across Experiments
• Meta-learning with Stochastic Linear Bandits
• Meta-Thompson Sampling