Avoiding the Price of Adaptivity: Inference in Linear Contextual Bandits via Stability
避免适应性的代价：基于稳定性的线性情境赌博机推断AI 解读 ↓
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避免适应性的代价：基于稳定性的线性情境赌博机推断
- 研究问题
- 在线性情境赌博机的自适应采样下，能否保持经典最小二乘区间的渐近有效性，同时获得接近最优的累积遗憾保证？
- 方法与思路
- 作者提出正则化 EXP4 算法，使经验特征协方差满足 Lai–Wei 稳定性条件，并分析中心极限定理与遗憾界。
- 材料陈述的贡献
- 摘要称，算法支持有效的 Wald 型区间及定量正态近似，并具有仅差对数因子的极小极大遗憾保证，还用于条件平均处理效应。
- 阅读关注点
- 核对稳定性条件、协方差极限及正则化选择，区间有效性的渐近范围，以及条件平均处理效应应用中的额外假设。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核验；摘要未列出数据生成条件、收敛界或模拟数值，保证不能推广到任意策略。
原文摘要
Statistical inference in contextual bandits is challenging due to the adaptive, non-i.i.d. nature of the data. A growing body of work shows that classical least-squares inference can fail under adaptive sampling, and that valid confidence intervals for linear functionals typically require an inflation of order $\sqrt{d \log T}$. This phenomenon -- often termed the price of adaptivity -- reflects the intrinsic difficulty of reliable inference under general contextual bandit policies. A key structural condition that overcomes this limitation is the stability condition of Lai and Wei, which requires the empirical feature covariance to converge to a deterministic limit. When stability holds, the ordinary least-squares estimator satisfies a central limit theorem, and classical Wald-type confidence intervals remain asymptotically valid under adaptation, without incurring the $\sqrt{d \log T}$ price of adaptivity. In this paper, we propose and analyze a regularized EXP4 algorithm for linear contextual bandits. Our first main result shows that this procedure satisfies the Lai--Wei stability condition and therefore admits valid Wald-type confidence intervals for linear functionals. We additionally provide quantitative rates of convergence in the associated central limit theorem. Our second result establishes that the same algorithm achieves regret guarantees that are minimax optimal up to logarithmic factors, demonstrating that stability and statistical efficiency can coexist within a single contextual bandit method. As an application of our theory, we show how it can be used to construct confidence intervals for the conditional average treatment effect (CATE) under adaptively collected data. Finally, we complement our theory with simulations illustrating the empirical normality of the resulting estimators and the sharpness of the corresponding confidence intervals.