  We study the use of policy gradient algorithms to optimize over a class of
generalized Thompson sampling policies. Our central insight is to view the
posterior parameter sampled by Thompson sampling as a kind of pseudo-action.
Policy gradient methods can then be tractably applied to search over a class of
sampling policies, which determine a probability distribution over
pseudo-actions (i.e., sampled parameters) as a function of observed data. We
also propose and compare policy gradient estimators that are specialized to
Bayesian bandit problems. Numerical experiments demonstrate that direct policy
search on top of Thompson sampling automatically corrects for some of the
algorithm's known shortcomings and offers meaningful improvements even in long
horizon problems where standard Thompson sampling is extremely effective.
