PAC-Bayes Bounds for Bandit Problems: A Survey and Experimental Comparison

TL;DR

This paper surveys PAC-Bayes bounds applied to bandit problems, compares their performance experimentally, and highlights their potential for offline algorithms with strong guarantees, while noting challenges in online settings.

Contribution

It provides the first comprehensive overview of PAC-Bayes bounds for bandits and experimentally compares their effectiveness in offline and online algorithms.

Findings

PAC-Bayes bounds are effective for offline bandit algorithms with performance guarantees.

Offline PAC-Bayesian algorithms learned neural network policies with competitive rewards.

Online PAC-Bayesian bandit algorithms showed loose regret bounds.

Abstract

PAC-Bayes has recently re-emerged as an effective theory with which one can derive principled learning algorithms with tight performance guarantees. However, applications of PAC-Bayes to bandit problems are relatively rare, which is a great misfortune. Many decision-making problems in healthcare, finance and natural sciences can be modelled as bandit problems. In many of these applications, principled algorithms with strong performance guarantees would be very much appreciated. This survey provides an overview of PAC-Bayes bounds for bandit problems and an experimental comparison of these bounds. On the one hand, we found that PAC-Bayes bounds are a useful tool for designing offline bandit algorithms with performance guarantees. In our experiments, a PAC-Bayesian offline contextual bandit algorithm was able to learn randomised neural network polices with competitive expected reward and non-vacuous performance guarantees. On the other hand, the PAC-Bayesian online bandit algorithms that we tested had loose cumulative regret bounds. We conclude by discussing some topics for future work on PAC-Bayesian bandit algorithms.