Variance-sensitive Thompson sampling for generalised linear bandits, revisited
It provides a theoretical improvement for Thompson sampling in generalised linear bandits, though the requirement of a warm-up phase limits its practical impact.
The paper proves a variance-sensitive regret bound for Thompson sampling in stochastic generalised linear bandits, using a warm-up phase and the Gaussian Poincaré inequality to bypass limitations of optimism-based analyses.
We prove a variance-sensitive regret bound for Thompson sampling in stochastic generalised linear bandits. The argument assumes a warm-up, after which the regret is controlled through using the Gaussian Poincaré inequality. This bypasses the point at which previous optimism-based analyses break down. Removing the warm-up while retaining the same variance-sensitive scaling remains open, and appears nontrivial.