Reproduce “Improved Regret Analysis in Gaussian Process Bandits: Optimality for Noiseless Reward, RKHS norm, and Non-Stationary Variance” on OpenResearch

About this paper

Shogo Iwazaki, Shion Takeno

This paper presents improved regret analyses for Gaussian Process (GP) bandit algorithms by deriving a tighter upper bound on maximum posterior variance. The work demonstrates that existing algorithms achieve near-optimal regret in noiseless settings, establish optimal dependence on the RKHS norm, and provides the first theoretical framework with lower and upper bounds for GP bandits under non-stationary observation noise.

Key insights

• A refined bound on the maximum posterior variance is crucial for achieving state-of-the-art regret guarantees, enabling existing simple algorithms like MVR and PE to reach near-optimal performance in challenging settings.
• Even with non-stationary observation noise, GP bandit algorithms can be adapted to achieve near-optimal, variance-dependent regret, bridging the gap between theoretical models and real-world dynamic noise environments.
• The proposed variance-aware MVR and PE algorithms effectively leverage knowledge of time-varying noise, demonstrably outperforming naive extensions of variance-aware linear bandit approaches in the kernelized setting.

Summary by alphaXiv.