# Adaptive Linear Estimating Equations

arXiv: https://arxiv.org/abs/2307.07320 · HTML: https://mlsanity.com/paper/2307.07320/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 14 Jul 2023.

## Builds on (most cited first, 18 of 18)

- [Confidence Intervals for Policy Evaluation in Adaptive Experiments](https://mlsanity.com/paper/1911.02768/) (2019)
- [Don't Judge an Object by Its Context: Learning to Overcome Contextual Bias](https://mlsanity.com/paper/2001.03152/) (2020)
- [Personalized HeartSteps: A Reinforcement Learning Algorithm for Optimizing Physical Activity](https://mlsanity.com/paper/1909.03539/) (2019)
- [Inference for Batched Bandits](https://mlsanity.com/paper/2002.03217/) (2020)
- [The End of Optimism? An Asymptotic Analysis of Finite-Armed Linear Bandits](https://mlsanity.com/paper/1610.04491/) (2016)
- [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)
- [On the bias, risk and consistency of sample means in multi-armed bandits](https://mlsanity.com/paper/1902.00746/) (2019)
- [Are sample means in multi-armed bandits positively or negatively biased?](https://mlsanity.com/paper/1905.11397/) (2019)
- [Online Multi-Armed Bandits with Adaptive Inference](https://mlsanity.com/paper/2102.13202/) (2021)
- [Mitigating Bias in Adaptive Data Gathering via Differential Privacy](https://mlsanity.com/paper/1806.02329/) (2018)
- [Policy Learning with Adaptively Collected Data](https://mlsanity.com/paper/2105.02344/) (2021)
- [Near-optimal inference in adaptive linear regression](https://mlsanity.com/paper/2107.02266/) (2021)
- [Online Debiasing for Adaptively Collected High-dimensional Data with Applications to Time Series Analysis](https://mlsanity.com/paper/1911.01040/) (2019)
- [Semi-parametric inference based on adaptively collected data](https://mlsanity.com/paper/2303.02534/) (2023)

## Built on by (most cited first, 6 of 6)

- [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 Off-Policy Inference for M-Estimators Under Model Misspecification](https://mlsanity.com/paper/2509.14218/) (2025)
- [Statistical Limits of Adaptive Linear Models: Low-Dimensional Estimation and Inference](https://mlsanity.com/paper/2310.00532/) (2023)
- [Bandit Simulation for Average Reward Inference](https://mlsanity.com/paper/2606.00913/) (2026)

## Abstract (arXiv)

Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference procedure. For instance, the ordinary least squares (OLS) estimator in an adaptive linear regression model can exhibit non-normal asymptotic behavior, posing challenges for accurate inference and interpretation. In this paper, we propose a general method for constructing debiased estimator which remedies this issue. It makes use of the idea of adaptive linear estimating equations, and we establish theoretical guarantees of asymptotic normality, supplemented by discussions on achieving near-optimal asymptotic variance. A salient feature of our estimator is that in the context of multi-armed bandits, our estimator retains the non-asymptotic performance of the least square estimator while obtaining asymptotic normality property. Consequently, this work helps connect two fruitful paradigms of adaptive inference: a) non-asymptotic inference using concentration inequalities and b) asymptotic inference via asymptotic normality.