Bridging the Gap between Empirical Welfare Maximization and Conditional Average Treatment Effect Estimation in Policy Learning
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连接政策学习中的经验福利最大化与条件平均处理效应估计
- 研究问题
- 经验福利最大化与先估计条件平均处理效应的政策学习方法有何关系，能否利用这种关系改善正则化与优化？
- 方法与思路
- 作者对政策类重新参数化，证明经验福利最大化与最小二乘优化的精确等价，并利用该关系构建平滑替代与正则化方法。
- 材料陈述的贡献
- 摘要称两类方法在共同条件下可共享理论保证，最小二乘转化有助于优化，同时明确许多政策类仍保留组合计算困难。
- 阅读关注点
- 应核对等价成立的目标函数和政策类变换、共同理论条件、正则化如何影响政策选择，以及平滑优化与精确求解的差别。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未列出完整条件，转化不能据此被解释为普遍解决精确优化的计算困难。
原文摘要
The goal of policy learning is to train a policy function that recommends a treatment given covariates to maximize population welfare. There are two major approaches in policy learning: the empirical welfare maximization (EWM) approach and the plug-in approach. The EWM approach is analogous to a classification problem, where one first builds an estimator of the population welfare, which is a functional of policy functions, and then trains a policy by maximizing the estimated welfare. In contrast, the plug-in approach is based on regression, where one first estimates the conditional average treatment effect (CATE) and then recommends the treatment with the highest estimated outcome. This study bridges the gap between the two approaches by showing that both are based on essentially the same optimization problem. In particular, we prove an exact equivalence between EWM and least squares over a reparameterization of the policy class. As a consequence, the two approaches are interchangeable in several respects and share the same theoretical guarantees under common conditions. Leveraging this equivalence, we propose a regularization method for policy learning. The reduction to least squares yields a smooth surrogate that is typically easier to optimize in practice. At the same time, for many natural policy classes the inherent combinatorial hardness of exact EWM generally remains, so the reduction should be viewed as an optimization aid rather than a universal bypass of NP-hardness.