Synthetic Control as Online Linear Regression
发现合成控制法与在线学习中的“跟随领导者”算法等价，并证明即使结果由对手选择，其反事实预测效果也接近最优加权平均，为比较案例研究提供了理论支持。
This paper notes a simple connection between synthetic control and online learning. Specifically, we recognize synthetic control as an instance of Follow‐The‐Leader (FTL). Standard results in online convex optimization then imply that, even when outcomes are chosen by an adversary, synthetic control predictions of counterfactual outcomes for the treated unit perform almost as well as an oracle weighted average of control units' outcomes. Synthetic control on differenced data performs almost as well as oracle weighted difference‐in‐differences, potentially making it an attractive choice in practice. We argue that this observation further supports the use of synthetic control estimators in comparative case studies.