Approximate Thompson Sampling with Langevin Algorithms

Jul 12, 2020



Thompson sampling has been demonstrated both theoretically and empirically to enjoy favorable performance in tackling multi-armed bandits problems. Despite its successes, however, one key obstacle to its use in a much broader range of scenarios is the need for perfect samples from posterior distributions at every iteration, which is oftentimes not feasible in practice. We propose a Markov Chain Monte Carlo (MCMC) method tailored to Thompson sampling to address this issue. We construct a fast converging Langevin algorithm to generate approximate samples with accuracy guarantees. We then leverage novel posterior concentration rates to analyze the statistical risk of the overall Thompson sampling method. Finally, we specify the necessary hyperparameters and the required computational resources for the MCMC procedure to match the optimal risk. The resulting algorithm enjoys both optimal instance-dependent frequentist regret and appealing computation complexity.



About ICML 2020

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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