mlsanityData to 14 Oct 2026

Adaptive Linear Estimating Equations

arXiv 2307.07320 ↗First posted 14 Jul 2023math.ST cs.LG stat.MLcited by 6

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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.

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

18 of 38 references.

References · 18

  1. 2019Confidence Intervals for Policy Evaluation in Adaptive Experimentscited by 95
  2. 2020Don't Judge an Object by Its Context: Learning to Overcome Contextual Biascited by 91
  3. 2019Personalized HeartSteps: A Reinforcement Learning Algorithm for Optimizing Physical Activitycited by 70
  4. 2020Inference for Batched Banditscited by 63
  5. 2016The End of Optimism? An Asymptotic Analysis of Finite-Armed Linear Banditscited by 49
  6. 2021Off-Policy Evaluation via Adaptive Weighting with Data from Contextual Banditscited by 40
  7. 2017Accurate Inference for Adaptive Linear Modelscited by 39
  8. 2016A Reinforcement Learning System to Encourage Physical Activity in Diabetes Patientscited by 38
  9. 2017Why Adaptively Collected Data Have Negative Bias and How to Correct for Itcited by 36
  10. 2021Post-Contextual-Bandit Inferencecited by 32
  11. 2019On the bias, risk and consistency of sample means in multi-armed banditscited by 25
  12. 2019Are sample means in multi-armed bandits positively or negatively biased?cited by 24
6 more
  1. 2021Online Multi-Armed Bandits with Adaptive Inferencecited by 22
  2. 2018Mitigating Bias in Adaptive Data Gathering via Differential Privacycited by 21
  3. 2021Policy Learning with Adaptively Collected Datacited by 21
  4. 2021Near-optimal inference in adaptive linear regressioncited by 21
  5. 2019Online Debiasing for Adaptively Collected High-dimensional Data with Applications to Time Series Analysiscited by 13
  6. 2023Semi-parametric inference based on adaptively collected datacited by 7

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 2; 2026: 1.

6 papers.

  1. 2024UCB algorithms for multi-armed bandits: Precise regret and adaptive inferencecited by 19
  2. 2024Inference with the Upper Confidence Bound Algorithmcited by 12
  3. 2025Stable Thompson Sampling: Valid Inference via Variance Inflationcited by 8
  4. 2025Adaptive Off-Policy Inference for M-Estimators Under Model Misspecificationcited by 4
  5. 2023Statistical Limits of Adaptive Linear Models: Low-Dimensional Estimation and Inferencecited by 3
  6. 2026Bandit Simulation for Average Reward Inferencecited by 0