  Stochastic sparse linear bandits offer a practical model for high-dimensional
online decision-making problems and have a rich information-regret structure.
In this work we explore the use of information-directed sampling (IDS), which
naturally balances the information-regret trade-off. We develop a class of
information-theoretic Bayesian regret bounds that nearly match existing lower
bounds on a variety of problem instances, demonstrating the adaptivity of IDS.
To efficiently implement sparse IDS, we propose an empirical Bayesian approach
for sparse posterior sampling using a spike-and-slab Gaussian-Laplace prior.
Numerical results demonstrate significant regret reductions by sparse IDS
relative to several baselines.
