In “Generalized Thompson sampling for sequential decision-making and causal inference“, Ortega and Braun (2013) give a short history of Thompson sampling (see , , , ) and report on the relationship between intelligent agents, evolutionary game theory, Bayesian inference, KL Divergence, and Thompson sampling. They develop a generalization of Thompson sampling based on a Bayesian prior over a distribution of environments. Some numerical results are provided. Here’s the abstract:
Recently, it has been shown how sampling actions from the predictive distribution over the optimal action—sometimes called Thompson sampling—can be applied to solve sequential adaptive control problems, when the optimal policy is known for each possible environment. The predictive distribution can then be constructed by a Bayesian superposition of the optimal policies weighted by their posterior probability that is updated by Bayesian inference and causal calculus. Here we discuss three important features of this approach. First, we discuss in how far such Thompson sampling can be regarded as a natural consequence of the Bayesian modeling of policy uncertainty. Second, we show how Thompson sampling can be used to study interactions between multiple adaptive agents, thus, opening up an avenue of game-theoretic analysis. Third, we show how Thompson sampling can be applied to infer causal relationships when interacting with an environment in a sequential fashion. In summary, our results suggest that Thompson sampling might not merely be a useful heuristic, but a principled method to address problems of adaptive sequential decision-making and causal inference.