PAC-Bayes Bounds for Bandit Problems: A Survey and Experimental Comparison
This work addresses the need for principled algorithms with performance guarantees in decision-making applications like healthcare and finance, but it is incremental as a survey and experimental comparison.
The paper surveys PAC-Bayes bounds for bandit problems, finding that they are useful for designing offline bandit algorithms with competitive expected rewards and non-vacuous guarantees, but online algorithms tested had loose cumulative regret bounds.
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.