We study counterfactual regression, which aims to map input features to outcomes under hypothetical scenarios that differ from those observed in the data. This is particularly useful for decision-making when adapting to sudden shifts in treatment patterns is essential. We propose a doubly robust-style estimator for counterfactual regression within a generalizable framework that accommodates a broad class of risk functions and flexible constraints, drawing on tools from semiparametric theory and stochastic optimization. Our approach uses incremental interventions to enhance adaptability while maintaining consistency with standard methods. We formulate the target estimand as the optimal solution to a stochastic optimization problem and develop an efficient estimation strategy, where we can leverage rapid development of modern optimization algorithms. We go on to analyze the rates of convergence and characterize the asymptotic distributions. Our analysis shows that the proposed estimators can achieve $\sqrt{n}$-consistency and asymptotic normality for a broad class of problems. Numerical illustrations highlight their effectiveness in adapting to unseen counterfactual scenarios while maintaining parametric convergence rates.

翻译：我们研究反事实回归，其目标是将输入特征映射到假设情境下的结果，这些情境与数据中观察到的情境不同。这在适应治疗模式的突然变化至关重要的决策过程中尤为有用。我们提出了一种双重稳健风格的估计器，用于反事实回归，该估计器基于一个可泛化的框架，该框架借鉴了半参数理论和随机优化的工具，能够容纳一大类风险函数和灵活的约束。我们的方法使用增量干预来增强适应性，同时保持与标准方法的一致性。我们将目标估计量表述为随机优化问题的最优解，并开发了一种高效的估计策略，该策略可以利用现代优化算法的快速发展。我们进一步分析了收敛速度并刻画了渐近分布。我们的分析表明，所提出的估计器对于一大类问题可以实现$\sqrt{n}$-相合性和渐近正态性。数值示例突显了其在适应未见反事实情境的同时保持参数收敛率的有效性。