# Fixed-Horizon Self-Normalized Inference for Adaptive Experiments via Martingale AIPW/DML with Logged Propensities

arXiv: https://arxiv.org/abs/2602.15559 · HTML: https://mlsanity.com/paper/2602.15559/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 34 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Builds on (most cited first, 14 of 14)

- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Doubly Robust Policy Evaluation and Optimization](https://mlsanity.com/paper/1503.02834/) (2015)
- [Multi-armed Bandit Models for the Optimal Design of Clinical Trials: Benefits and Challenges](https://mlsanity.com/paper/1507.08025/) (2015)
- [Confidence Intervals for Policy Evaluation in Adaptive Experiments](https://mlsanity.com/paper/1911.02768/) (2019)
- [Inference for Batched Bandits](https://mlsanity.com/paper/2002.03217/) (2020)
- [Off-Policy Evaluation via Adaptive Weighting with Data from Contextual Bandits](https://mlsanity.com/paper/2106.02029/) (2021)
- [Post-Contextual-Bandit Inference](https://mlsanity.com/paper/2106.00418/) (2021)
- [Time-uniform central limit theory and asymptotic confidence sequences](https://mlsanity.com/paper/2103.06476/) (2021)
- [Efficient Adaptive Experimental Design for Average Treatment Effect Estimation](https://mlsanity.com/paper/2002.05308/) (2020)
- [Semiparametric Efficient Inference in Adaptive Experiments](https://mlsanity.com/paper/2311.18274/) (2023)
- [Double machine learning and design in batch adaptive experiments](https://mlsanity.com/paper/2309.15297/) (2023)
- [Kernel Treatment Effects with Adaptively Collected Data](https://mlsanity.com/paper/2510.10245/) (2025)
- [Design Stability in Adaptive Experiments: Implications for Treatment Effect Estimation](https://mlsanity.com/paper/2510.22351/) (2025)

## Abstract (arXiv)

Adaptive randomized experiments update treatment probabilities as data accrue, but still require an end-of-study interval for the average treatment effect (ATE) at a prespecified horizon. Under adaptive assignment, propensities can keep changing, so the predictable quadratic variation of AIPW/DML score increments may remain random. When no deterministic variance limit exists, Wald statistics normalized by a single long-run variance target can be conditionally miscalibrated given the realized variance regime. We assume no interference, sequential randomization, i.i.d. arrivals, and executed overlap on a prespecified scored set, and we require two auditable pipeline conditions: the platform logs the executed randomization probability for each unit, and the nuisance regressions used to score unit t are constructed predictably from past data only. These conditions make the centered AIPW/DML scores an exact martingale difference sequence. Using self-normalized martingale limit theory, we show that the Studentized statistic, with variance estimated by realized quadratic variation, is asymptotically N(0,1) at the prespecified horizon, even without variance stabilization. Simulations validate the theory and highlight when standard fixed-variance Wald reporting fails.