提出新算法使处理效应估计误差随时间对数增长，显著优于旧方法。
Logarithmic Neyman Regret for Adaptive Estimation of the Average Treatment Effect
- 通过截断二阶矩追踪机制自适应调整处理分配概率。
- 在有限样本下实现奈曼悔悟的对数级增长，优于原有平方根级依赖。
- 适合需要高效因果推断的实际场景，如医疗试验与强化学习评估。
平均处理效应（ATE）估计是因果推断的核心问题，与强化学习中的离策略评估密切相关。本文研究自适应选择处理分配概率以优化ATE估计的问题。现有工作多关注渐近性质，忽视了实际中学习最优分配的难度及超参数选择问题。已有非渐近方法存在性能差、奈曼悔悟随问题参数指数增长的缺陷。为此，本文提出并分析了剪裁二阶矩追踪（ClipSMT）算法，该算法基于具有强渐近最优性的已有方法，给出了其奈曼悔悟的有限样本上界。分析表明，ClipSMT在两方面实现指数级改进：将对时间 $T$ 的依赖从 $O(\ ext{\sqrt{T}})$ 改进为 $O(\log T)$，并将问题参数的指数依赖降为多项式依赖。最后，仿真结果展示了ClipSMT相对于现有方法的显著优势。
原文摘要 · Abstract (English)
Estimation of the Average Treatment Effect (ATE) is a core problem in causal inference with strong connections to Off-Policy Evaluation in Reinforcement Learning. This paper considers the problem of adaptively selecting the treatment allocation probability in order to improve estimation of the ATE. The majority of prior work on adaptive ATE estimation focus on asymptotic guarantees, and in turn overlooks important practical considerations such as the difficulty of learning the optimal treatment allocation as well as hyper-parameter selection. Existing non-asymptotic methods are limited by poor empirical performance and exponential scaling of the Neyman regret with respect to problem parameters. In order to address these gaps, we propose and analyze the Clipped Second Moment Tracking (ClipSMT) algorithm, a variant of an existing algorithm with strong asymptotic optimality guarantees, and provide finite sample bounds on its Neyman regret. Our analysis shows that ClipSMT achieves exponential improvements in Neyman regret on two fronts: improving the dependence on $T$ from $O(\sqrt{T})$ to $O(\log T)$, as well as reducing the exponential dependence on problem parameters to a polynomial dependence. Finally, we conclude with simulations which show the marked improvement of ClipSMT over existing approaches.
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