# Semi-parametric inference based on adaptively collected data

arXiv: https://arxiv.org/abs/2303.02534 · HTML: https://mlsanity.com/paper/2303.02534/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 65 references that are in the map.
- First posted on arXiv 5 Mar 2023.

## Builds on (most cited first, 25 of 25)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [On the Complexity of Best Arm Identification in Multi-Armed Bandit Models](https://mlsanity.com/paper/1407.4443/) (2014)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [lil' UCB : An Optimal Exploration Algorithm for Multi-Armed Bandits](https://mlsanity.com/paper/1312.7308/) (2013)
- [Confidence Intervals for Policy Evaluation in Adaptive Experiments](https://mlsanity.com/paper/1911.02768/) (2019)
- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [Inference for Batched Bandits](https://mlsanity.com/paper/2002.03217/) (2020)
- [Orthogonal Random Forest for Causal Inference](https://mlsanity.com/paper/1806.03467/) (2018)
- [Sparsity-Agnostic Lasso Bandit](https://mlsanity.com/paper/2007.08477/) (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)
- [Accurate Inference for Adaptive Linear Models](https://mlsanity.com/paper/1712.06695/) (2017)
- [A Reinforcement Learning System to Encourage Physical Activity in Diabetes Patients](https://mlsanity.com/paper/1605.04070/) (2016)
- [Why Adaptively Collected Data Have Negative Bias and How to Correct for It](https://mlsanity.com/paper/1708.01977/) (2017)
- [Post-Contextual-Bandit Inference](https://mlsanity.com/paper/2106.00418/) (2021)
- [Double/Debiased Machine Learning for Dynamic Treatment Effects via g-Estimation](https://mlsanity.com/paper/2002.07285/) (2020)
- [Near-optimal inference in adaptive linear regression](https://mlsanity.com/paper/2107.02266/) (2021)
- [Reward Design For An Online Reinforcement Learning Algorithm Supporting Oral Self-Care](https://mlsanity.com/paper/2208.07406/) (2022)
- [Post-Selection Inference for Generalized Linear Models with Many Controls](https://mlsanity.com/paper/1304.3969/) (2013)
- [Evaluating (weighted) dynamic treatment effects by double machine learning](https://mlsanity.com/paper/2012.00370/) (2020)
- [Double/Debiased Machine Learning for Logistic Partially Linear Model](https://mlsanity.com/paper/2009.14461/) (2020)
- [Post Reinforcement Learning Inference](https://mlsanity.com/paper/2302.08854/) (2023)

## Built on by (most cited first, 7 of 7)

- [UCB algorithms for multi-armed bandits: Precise regret and adaptive inference](https://mlsanity.com/paper/2412.06126/) (2024)
- [Inference with the Upper Confidence Bound Algorithm](https://mlsanity.com/paper/2408.04595/) (2024)
- [Stable Thompson Sampling: Valid Inference via Variance Inflation](https://mlsanity.com/paper/2505.23260/) (2025)
- [Adaptive Linear Estimating Equations](https://mlsanity.com/paper/2307.07320/) (2023)
- [Statistical Limits of Adaptive Linear Models: Low-Dimensional Estimation and Inference](https://mlsanity.com/paper/2310.00532/) (2023)
- [Online Data Collection for Efficient Semiparametric Inference](https://mlsanity.com/paper/2411.03195/) (2024)
- [Statistical Inference for Misspecified Contextual Bandits](https://mlsanity.com/paper/2606.22639/) (2026)

## Abstract (arXiv)

Many standard estimators, when applied to adaptively collected data, fail to be asymptotically normal, thereby complicating the construction of confidence intervals. We address this challenge in a semi-parametric context: estimating the parameter vector of a generalized linear regression model contaminated by a non-parametric nuisance component. We construct suitably weighted estimating equations that account for adaptivity in data collection, and provide conditions under which the associated estimates are asymptotically normal. Our results characterize the degree of "explorability" required for asymptotic normality to hold. For the simpler problem of estimating a linear functional, we provide similar guarantees under much weaker assumptions. We illustrate our general theory with concrete consequences for various problems, including standard linear bandits and sparse generalized bandits, and compare with other methods via simulation studies.