提出方向稳定性条件，让自适应实验后推断更高效可靠。
Efficient Inference after Directionally Stable Adaptive Experiments
- 引入方向稳定性，比旧条件更宽松且针对性强。
- 证明在自适应数据下估计量仍具渐近正态性和效率。
- 首次为LinUCB算法提供半参数效率保证，适合研究者参考。
我们研究在自适应数据收集（如多臂赌博机）后对路径可微标量目标的推断问题。提出一种新的目标特定条件——方向稳定性，该条件严格弱于以往无目标依赖的稳定性假设。在方向稳定性下，即使在自适应轨迹中计算，原本在独立同分布数据下有效的估计量仍保持渐近正态性和半参数效率。其经典梯度具有鞅形式，方向稳定性确保其可预测二次变差的稳定化，从而实现高维渐近正态性。通过卷积定理刻画效率，并给出一步估计量达到效率界限的条件。验证了线性上下文赌博机（LinUCB）满足方向稳定性，首次为常规标量目标在LinUCB采样下提供了半参数效率保证。
原文摘要 · Abstract (English)
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.
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