Kernel Treatment Effects with Adaptively Collected Data
This addresses the challenge of analyzing complex treatment effects beyond averages in adaptive experiments, which is important for fields like causal inference and clinical trials, though it builds on existing kernel and doubly robust methods.
The paper tackles the problem of conducting distributional inference for treatment effects under adaptive data collection, where traditional methods fail due to broken i.i.d. assumptions, and presents a kernel-based framework that ensures asymptotic normality and valid type-I error, with experiments showing it outperforms adaptive baselines limited to scalar effects.
Adaptive experiments improve efficiency by adjusting treatment assignments based on past outcomes, but this adaptivity breaks the i.i.d. assumptions that underpins classical asymptotics. At the same time, many questions of interest are distributional, extending beyond average effects. Kernel treatment effects (KTE) provide a flexible framework by representing counterfactual outcome distributions in an RKHS and comparing them via kernel distances. We present the first kernel-based framework for distributional inference under adaptive data collection. Our method combines doubly robust scores with variance stabilization to ensure asymptotic normality via a Hilbert-space martingale CLT, and introduces a sample-fitted stabilized test with valid type-I error. Experiments show it is well calibrated and effective for both mean shifts and higher-moment differences, outperforming adaptive baselines limited to scalar effects.