VITS : Variational Inference Thompson Sampling for contextual bandits

TL;DR

This paper introduces VITS, a variational inference-based Thompson sampling algorithm for contextual bandits, offering efficient posterior approximation and sub-linear regret bounds, with demonstrated effectiveness on synthetic and real datasets.

Contribution

We propose VITS, a novel variational inference approach for Thompson sampling that improves computational efficiency and maintains theoretical regret guarantees.

Findings

VITS achieves sub-linear regret comparable to traditional TS.

VITS provides accurate posterior approximations efficiently.

Experimental results show VITS outperforms existing methods on datasets.

Abstract

In this paper, we introduce and analyze a variant of the Thompson sampling (TS) algorithm for contextual bandits. At each round, traditional TS requires samples from the current posterior distribution, which is usually intractable. To circumvent this issue, approximate inference techniques can be used and provide samples with distribution close to the posteriors. However, current approximate techniques yield to either poor estimation (Laplace approximation) or can be computationally expensive (MCMC methods, Ensemble sampling...). In this paper, we propose a new algorithm, Varational Inference Thompson sampling VITS, based on Gaussian Variational Inference. This scheme provides powerful posterior approximations which are easy to sample from, and is computationally efficient, making it an ideal choice for TS. In addition, we show that VITS achieves a sub-linear regret bound of the same order in the dimension and number of round as traditional TS for linear contextual bandit. Finally, we demonstrate experimentally the effectiveness of VITS on both synthetic and real world datasets.