# Synthetic Control As Online Linear Regression

arXiv: https://arxiv.org/abs/2202.08426 · HTML: https://mlsanity.com/paper/2202.08426/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 46 references that are in the map.
- First posted on arXiv 17 Feb 2022.

## Builds on (most cited first, 12 of 12)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Synthetic Difference in Differences](https://mlsanity.com/paper/1812.09970/) (2018)
- [An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls](https://mlsanity.com/paper/1712.09089/) (2017)
- [Online Learning with Optimism and Delay](https://mlsanity.com/paper/2106.06885/) (2021)
- [The Augmented Synthetic Control Method](https://mlsanity.com/paper/1811.04170/) (2018)
- [On the Assumptions of Synthetic Control Methods](https://mlsanity.com/paper/2112.05671/) (2021)
- [Synthetic learner: model-free inference on treatments over time](https://mlsanity.com/paper/1904.01490/) (2019)
- [A Design-Based Perspective on Synthetic Control Methods](https://mlsanity.com/paper/2101.09398/) (2021)
- [Synthetic Controls with Staggered Adoption](https://mlsanity.com/paper/1912.03290/) (2019)

## Built on by (most cited first, 5 of 5)

- [Adaptive Principal Component Regression with Applications to Panel Data](https://mlsanity.com/paper/2307.01357/) (2023)
- [Tangential Wasserstein Projections](https://mlsanity.com/paper/2207.14727/) (2022)
- [Weighted Sum-Rate Maximization With Causal Inference for Latent Interference Estimation](https://mlsanity.com/paper/2211.08327/) (2022)
- [Bounded (O(1)) Regret Recommendation Learning via Synthetic Controls Oracle](https://mlsanity.com/paper/2301.12571/) (2023)
- [Incentive-Aware Synthetic Control: Accurate Counterfactual Estimation via Incentivized Exploration](https://mlsanity.com/paper/2312.16307/) (2023)

## Abstract (arXiv)

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.