Online Posterior Sampling with a Diffusion Prior

TL;DR

This paper introduces approximate posterior sampling algorithms for contextual bandits using diffusion model priors, combining the efficiency of Gaussian priors with the ability to model complex distributions, and demonstrates their effectiveness empirically.

Contribution

It proposes a novel method for posterior sampling in contextual bandits with diffusion priors, extending the Laplace approximation approach to more complex distributions.

Findings

Algorithms are asymptotically consistent.

Perform well empirically on various bandit problems.

Maintain simplicity and efficiency of Gaussian prior methods.

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.