# Efficient Inference after Directionally Stable Adaptive Experiments

arXiv: https://arxiv.org/abs/2602.21478 · HTML: https://mlsanity.com/paper/2602.21478/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 38 references that are in the map.
- First posted on arXiv 25 Feb 2026.

## Builds on (most cited first, 19 of 19)

- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [Confidence Intervals for Policy Evaluation in Adaptive Experiments](https://mlsanity.com/paper/1911.02768/) (2019)
- [Statistical Inference with M-Estimators on Adaptively Collected Data](https://mlsanity.com/paper/2104.14074/) (2021)
- [Post-Contextual-Bandit Inference](https://mlsanity.com/paper/2106.00418/) (2021)
- [A Closer Look at the Worst-case Behavior of Multi-armed Bandit Algorithms](https://mlsanity.com/paper/2106.02126/) (2021)
- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [UCB algorithms for multi-armed bandits: Precise regret and adaptive inference](https://mlsanity.com/paper/2412.06126/) (2024)
- [Efficient online learning with kernels for adversarial large scale problems](https://mlsanity.com/paper/1902.09917/) (2019)
- [The Typical Behavior of Bandit Algorithms](https://mlsanity.com/paper/2210.05660/) (2022)
- [Inference with the Upper Confidence Bound Algorithm](https://mlsanity.com/paper/2408.04595/) (2024)
- [Near-Optimal Non-Parametric Sequential Tests and Confidence Sequences with Possibly Dependent Observations](https://mlsanity.com/paper/2212.14411/) (2022)
- [Stable Thompson Sampling: Valid Inference via Variance Inflation](https://mlsanity.com/paper/2505.23260/) (2025)
- [Adaptive debiased machine learning using data-driven model selection techniques](https://mlsanity.com/paper/2307.12544/) (2023)
- [Statistical Inference under Adaptive Sampling with LinUCB](https://mlsanity.com/paper/2512.00222/) (2025)
- [Thompson sampling: Precise arm-pull dynamics and adaptive inference](https://mlsanity.com/paper/2601.21131/) (2026)
- [Nonparametric Instrumental Variable Inference with Many Weak Instruments](https://mlsanity.com/paper/2505.07729/) (2025)
- [Allocation Stability and Wald Inference under Variance-Aware UCB](https://mlsanity.com/paper/2412.08843/) (2024)
- [Simulation-Based Inference for Adaptive Experiments](https://mlsanity.com/paper/2506.02881/) (2025)
- [Optimal tests following sequential experiments](https://mlsanity.com/paper/2305.00403/) (2023)

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

- [Bandit Simulation for Average Reward Inference](https://mlsanity.com/paper/2606.00913/) (2026)

## Abstract (arXiv)

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.