Reproduce “Kernel Single-Index Bandits: Estimation, Inference, and Learning” on OpenResearch

About this paper

Sakshi Arya, Satarupa Bhattacharjee, Bharath K. Sriperumbudur

K-SIEGE estimates arm-specific context directions and flexible reward curves in contextual bandits with adaptive feedback. It uses inverse-propensity weighting and a known context score to estimate directions, then kernel regression to fit curves over projected contexts. In simulation, its pointwise intervals approached nominal 95% coverage and were three to five times shorter than Arya–Sriperumbudur’s uniform bands.

Key insights

• Asymptotic normality for the index parameter estimator (β̂ᵢ) can be established in an adaptive sampling context by using Stein's identity and IPW, providing a basis for parametric inference.
• A directional functional Central Limit Theorem (FCLT) can be derived for the nonparametric link function estimator (f̂ᵢ) in RKHS, enabling pointwise confidence intervals for adaptively learned functions.
• Robust statistical inference for both parametric and nonparametric components is achievable concurrently with competitive regret minimization within a single online learning framework.

Summary by alphaXiv.