Scalable Thompson Sampling via Optimal Transport

Thompson sampling (TS) is a class of algorithms for sequential decision-making, which requires maintaining a posterior distribution over a reward model. However, calculating exact posterior distributions is intractable for all but the simplest models. Consequently, how to computationally-efficiently approximate a posterior distribution is a crucial problem for scalable TS with complex models, such as neural networks. In this paper, we use distribution optimization techniques to approximate the posterior distribution, solved via Wasserstein gradient flows. Based on the framework, a principled particle-optimization algorithm is developed for TS to approximate the posterior efficiently. Our approach is scalable and does not make explicit distribution assumptions on posterior approximations. Extensive experiments on both synthetic data and large-scale real data demonstrate the superior performance of the proposed methods.