Thompson Sampling for High-Dimensional Sparse Linear Contextual Bandits
This work addresses the challenge of efficient decision-making in high-dimensional settings for applications like recommendation systems, though it is incremental as it extends Thompson sampling with known techniques.
The paper tackles the problem of high-dimensional sparse linear contextual bandits by analyzing Thompson sampling with sparsity-inducing priors, achieving a nearly optimal regret bound and demonstrating improved performance in simulations.
We consider the stochastic linear contextual bandit problem with high-dimensional features. We analyze the Thompson sampling algorithm using special classes of sparsity-inducing priors (e.g., spike-and-slab) to model the unknown parameter and provide a nearly optimal upper bound on the expected cumulative regret. To the best of our knowledge, this is the first work that provides theoretical guarantees of Thompson sampling in high-dimensional and sparse contextual bandits. For faster computation, we use variational inference instead of Markov Chain Monte Carlo (MCMC) to approximate the posterior distribution. Extensive simulations demonstrate the improved performance of our proposed algorithm over existing ones.