VITS : Variational Inference Thompson Sampling for contextual bandits
This work addresses a computational bottleneck in contextual bandits for researchers and practitioners, offering an incremental improvement over existing approximate inference methods.
The paper tackles the computational intractability of Thompson sampling in contextual bandits by proposing VITS, a method based on Gaussian variational inference that achieves sub-linear regret comparable to traditional Thompson sampling while being computationally efficient.
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.