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[2602.21478] Efficient Inference after Directionally Stable Adaptive Experiments
Summary
This paper explores efficient inference methods for adaptive experiments, introducing the concept of directional stability, which enhances the reliability of estimators derived from adaptive data collection methods like bandit algorithms.
Why It Matters
The research addresses a significant gap in statistical methodology by providing conditions under which adaptive data collection can yield efficient estimators. This is crucial for fields utilizing adaptive experiments, such as machine learning and statistics, where accurate inference is essential for decision-making.
Key Takeaways
- Introduces directional stability, a weaker condition than previously used stability criteria.
- Demonstrates that estimators remain efficient under adaptive data collection.
- Provides the first semiparametric efficiency guarantee for LinUCB sampling.
- Establishes a convolution theorem for characterizing efficiency in adaptive data settings.
- Highlights the martingale form of the canonical gradient for high-dimensional asymptotic normality.
Statistics > Machine Learning arXiv:2602.21478 (stat) [Submitted on 25 Feb 2026] Title:Efficient Inference after Directionally Stable Adaptive Experiments Authors:Zikai Shen, Houssam Zenati, Nathan Kallus, Arthur Gretton, Koulik Khamaru, Aurélien Bibaut View a PDF of the paper titled Efficient Inference after Directionally Stable Adaptive Experiments, by Zikai Shen and 5 other authors View PDF HTML (experimental) Abstract:We study inference on scalar-valued pathwise differentiable targets after adaptive data collection, such as a bandit algorithm. We introduce a novel target-specific condition, directional stability, which is strictly weaker than previously imposed target-agnostic stability conditions. Under directional stability, we show that estimators that would have been efficient under i.i.d. data remain asymptotically normal and semiparametrically efficient when computed from adaptively collected trajectories. The canonical gradient has a martingale form, and directional stability guarantees stabilization of its predictable quadratic variation, enabling high-dimensional asymptotic normality. We characterize efficiency using a convolution theorem for the adaptive-data setting, and give a condition under which the one-step estimator attains the efficiency bound. We verify directional stability for LinUCB, yielding the first semiparametric efficiency guarantee for a regular scalar target under LinUCB sampling. Comments: Subjects: Machine Learning (stat.ML); Machine Lear...
