Online Posterior Sampling with a Diffusion Prior

Branislav Kveton, Boris N. Oreshkin, Youngsuk Park, Aniket Anand Deshmukh, Rui Song

Keywords: posterior sampling, diffusion models, online learning, contextual bandits

TL;DR: We propose Laplace posterior sampling approximations for linear models and GLMs with a diffusion model prior, and apply them to contextual bandits.

Abstract: Posterior sampling in contextual bandits with a Gaussian prior can be implemented exactly or approximately using the Laplace approximation. The Gaussian prior is computationally efficient but it cannot describe complex distributions. In this work, we propose approximate posterior sampling algorithms for contextual bandits with a diffusion model prior. The key idea is to sample from a chain of approximate conditional posteriors, one for each stage of the reverse diffusion process, which are obtained by the Laplace approximation. Our approximations are motivated by posterior sampling with a Gaussian prior, and inherit its simplicity and efficiency. They are asymptotically consistent and perform well empirically on a variety of contextual bandit problems.

Primary Area: Bandits

Submission Number: 5528