# Demistifying Inference after Adaptive Experiments

arXiv: https://arxiv.org/abs/2405.01281 · HTML: https://mlsanity.com/paper/2405.01281/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 2 May 2024.

## Builds on (most cited first, 13 of 13)

- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [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)
- [Statistical Inference with M-Estimators on Adaptively Collected Data](https://mlsanity.com/paper/2104.14074/) (2021)
- [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)
- [Dynamic Pricing with Demand Covariates](https://mlsanity.com/paper/1604.07463/) (2016)
- [Applied Causal Inference Powered by ML and AI](https://mlsanity.com/paper/2403.02467/) (2024)
- [Time-uniform central limit theory and asymptotic confidence sequences](https://mlsanity.com/paper/2103.06476/) (2021)
- [Dynamic Assortment Personalization in High Dimensions](https://mlsanity.com/paper/1610.05604/) (2016)
- [Risk Minimization from Adaptively Collected Data: Guarantees for Supervised and Policy Learning](https://mlsanity.com/paper/2106.01723/) (2021)
- [Contextual Bandits in a Survey Experiment on Charitable Giving: Within-Experiment Outcomes versus Policy Learning](https://mlsanity.com/paper/2211.12004/) (2022)
- [Optimal tests following sequential experiments](https://mlsanity.com/paper/2305.00403/) (2023)

## Built on by (most cited first, 1 of 1)

- [GAAVI: Global Asymptotic Anytime Valid Inference for the Conditional Mean Function](https://mlsanity.com/paper/2602.08096/) (2026)

## Abstract (arXiv)

Adaptive experiments such as multi-arm bandits adapt the treatment-allocation policy and/or the decision to stop the experiment to the data observed so far. This has the potential to improve outcomes for study participants within the experiment, to improve the chance of identifying best treatments after the experiment, and to avoid wasting data. Seen as an experiment (rather than just a continually optimizing system) it is still desirable to draw statistical inferences with frequentist guarantees. The concentration inequalities and union bounds that generally underlie adaptive experimentation algorithms can yield overly conservative inferences, but at the same time the asymptotic normality we would usually appeal to in non-adaptive settings can be imperiled by adaptivity. In this article we aim to explain why, how, and when adaptivity is in fact an issue for inference and, when it is, understand the various ways to fix it: reweighting to stabilize variances and recover asymptotic normality, always-valid inference based on joint normality of an asymptotic limiting sequence, and characterizing and inverting the non-normal distributions induced by adaptivity.