# Kernel Treatment Effects with Adaptively Collected Data

arXiv: https://arxiv.org/abs/2510.10245 · HTML: https://mlsanity.com/paper/2510.10245/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 68 references that are in the map.
- First posted on arXiv 11 Oct 2025.

## Builds on (most cited first, 19 of 19)

- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016)
- [Confidence Intervals for Policy Evaluation in Adaptive Experiments](https://mlsanity.com/paper/1911.02768/) (2019)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Inference for Batched Bandits](https://mlsanity.com/paper/2002.03217/) (2020)
- [Optimal Rates for Regularized Conditional Mean Embedding Learning](https://mlsanity.com/paper/2208.01711/) (2022)
- [Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression](https://mlsanity.com/paper/2102.08208/) (2021)
- [Statistical Inference with M-Estimators on Adaptively Collected Data](https://mlsanity.com/paper/2104.14074/) (2021)
- [Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves](https://mlsanity.com/paper/2010.04855/) (2020)
- [Counterfactual Mean Embeddings](https://mlsanity.com/paper/1805.08845/) (2018)
- [Post-Contextual-Bandit Inference](https://mlsanity.com/paper/2106.00418/) (2021)
- [Off-Policy Risk Assessment in Contextual Bandits](https://mlsanity.com/paper/2104.08977/) (2021)
- [Dimension-agnostic inference using cross U-statistics](https://mlsanity.com/paper/2011.05068/) (2020)
- [A Permutation-Free Kernel Independence Test](https://mlsanity.com/paper/2212.09108/) (2022)
- [One-Step Estimation of Differentiable Hilbert-Valued Parameters](https://mlsanity.com/paper/2303.16711/) (2023)
- [An Efficient Doubly-Robust Test for the Kernel Treatment Effect](https://mlsanity.com/paper/2304.13237/) (2023)
- [Sequential Counterfactual Risk Minimization](https://mlsanity.com/paper/2302.12120/) (2023)
- [Doubly-Robust Estimation of Counterfactual Policy Mean Embeddings](https://mlsanity.com/paper/2506.02793/) (2025)
- [Double Debiased Machine Learning for Mediation Analysis with Continuous Treatments](https://mlsanity.com/paper/2503.06156/) (2025)

## Built on by (most cited first, 2 of 2)

- [Semiparametric Efficient Test for Interpretable Distributional Treatment Effects](https://mlsanity.com/paper/2605.08034/) (2026)
- [Fixed-Horizon Self-Normalized Inference for Adaptive Experiments via Martingale AIPW/DML with Logged Propensities](https://mlsanity.com/paper/2602.15559/) (2026)

## Abstract (arXiv)

Adaptive experiments improve efficiency by adjusting treatment assignments based on past outcomes, but this adaptivity breaks the i.i.d. assumptions that underpin 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 interventional 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 RKHS scores with a witness function learned on one fold, and performs inference on a second fold using a projected, sequentially normalized scalar statistic with valid type-I error. Experiments show that the resulting procedure is well calibrated and effective for both mean shifts and higher-moment differences, outperforming adaptive baselines limited to scalar effects.