Publication
PAC-Bayes Bounds for Bandit Problems: A Survey and Experimental Comparison
Hamish Flynn; David Reeb; Melih Kandemir; Jan Peters
In: IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), Vol. 45, No. 12, Pages 15308-15327, arXiv, 2023.
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.