Statistical Inference for Continuous Action Bandits

2026-10-07

AI Summary

This study addresses the lack of statistical inference methods for adaptively collected data with continuous actions. To bridge this gap, we extend kernel-smoothed doubly robust estimation to continuous action settings and propose an adaptive weighting estimator. The core contribution lies in establishing the first comprehensive statistical inference framework for such data, rigorously deriving the mean squared error convergence rate and asymptotic normality of the proposed estimator. Furthermore, by integrating regret analysis, this work provides theoretical guidance on experimental design efficiency. Extensive simulation studies validate the effectiveness of the proposed methodology.

Abstract

Statistical inference under adaptively collected data is becoming increasingly popular across e-commerce and mobile health. Many methods exist for discrete action settings, ranging from weighting to debiasing approaches. Despite the ubiquity of continuous actions in experimentation from optimal pricing to precision dosing, to the best of our knowledge, methods that support statistical inference under continuous action, adaptively collected data remain underdeveloped. In this work, we extend kernel-smoothed doubly robust estimation from i.i.d. data to adaptively collected data with continuous actions. We study a family of adaptively weighted estimators, establish their mean squared error rates, asymptotic normality, and characterize an estimation lower bound as a function of regret. We conclude with recommendations for experimental design informing efficiency and regret, and support our theory with an extensive simulation study.

Problem

• Continuous Action Bandits
• Statistical Inference
• Adaptively Collected Data
• Doubly Robust Estimation

Innovation

• Continuous Action Bandits
• Doubly Robust Estimation
• Adaptive Data
• Statistical Inference
• Kernel Smoothing