# Synthetically Controlled Bandits

arXiv: https://arxiv.org/abs/2202.07079 · HTML: https://mlsanity.com/paper/2202.07079/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 74 references that are in the map.
- First posted on arXiv 14 Feb 2022.

## Builds on (most cited first, 23 of 23)

- [Multi-armed Bandit Models for the Optimal Design of Clinical Trials: Benefits and Challenges](https://mlsanity.com/paper/1507.08025/) (2015)
- [Spectral Methods for Data Science: A Statistical Perspective](https://mlsanity.com/paper/2012.08496/) (2020)
- [Confidence Intervals for Policy Evaluation in Adaptive Experiments](https://mlsanity.com/paper/1911.02768/) (2019)
- [Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution](https://mlsanity.com/paper/1711.10467/) (2017)
- [Sequential Batch Learning in Finite-Action Linear Contextual Bandits](https://mlsanity.com/paper/2004.06321/) (2020)
- [Meta-Thompson Sampling](https://mlsanity.com/paper/2102.06129/) (2021)
- [Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization](https://mlsanity.com/paper/1902.07698/) (2019)
- [Regret Bounds for Batched Bandits](https://mlsanity.com/paper/1910.04959/) (2019)
- [The State of Applied Econometrics - Causality and Policy Evaluation](https://mlsanity.com/paper/1607.00699/) (2016)
- [Synthetic Difference in Differences](https://mlsanity.com/paper/1812.09970/) (2018)
- [Bandits with Switching Costs: T^{2/3} Regret](https://mlsanity.com/paper/1310.2997/) (2013)
- [Accurate Inference for Adaptive Linear Models](https://mlsanity.com/paper/1712.06695/) (2017)
- [Design and Analysis of Switchback Experiments](https://mlsanity.com/paper/2009.00148/) (2020)
- [Why Adaptively Collected Data Have Negative Bias and How to Correct for It](https://mlsanity.com/paper/1708.01977/) (2017)
- [An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls](https://mlsanity.com/paper/1712.09089/) (2017)
- [Post-Contextual-Bandit Inference](https://mlsanity.com/paper/2106.00418/) (2021)
- [On Robustness of Principal Component Regression](https://mlsanity.com/paper/1902.10920/) (2019)
- [Robust Synthetic Control](https://mlsanity.com/paper/1711.06940/) (2017)
- [The Augmented Synthetic Control Method](https://mlsanity.com/paper/1811.04170/) (2018)
- [Model-free Nonconvex Matrix Completion: Local Minima Analysis and Applications in Memory-efficient Kernel PCA](https://mlsanity.com/paper/1711.01742/) (2017)
- [Learning Treatment Effects in Panels with General Intervention Patterns](https://mlsanity.com/paper/2106.02780/) (2021)
- [Synthetic Controls for Experimental Design](https://mlsanity.com/paper/2108.02196/) (2021)
- [mRSC: Multi-dimensional Robust Synthetic Control](https://mlsanity.com/paper/1905.06400/) (2019)

## Built on by (most cited first, 8 of 8)

- [On the Sublinear Regret of GP-UCB](https://mlsanity.com/paper/2307.07539/) (2023)
- [Markovian Interference in Experiments](https://mlsanity.com/paper/2206.02371/) (2022)
- [Adaptive Experimentation in the Presence of Exogenous Nonstationary Variation](https://mlsanity.com/paper/2202.09036/) (2022)
- [Adaptive Principal Component Regression with Applications to Panel Data](https://mlsanity.com/paper/2307.01357/) (2023)
- [Adaptive Experiment Design with Synthetic Controls](https://mlsanity.com/paper/2401.17205/) (2024)
- [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)
- [Experimentation and Commitment under Reward Shifts](https://mlsanity.com/paper/2607.23432/) (2026)

## Abstract (arXiv)

This paper presents a new dynamic approach to experiment design in settings where, due to interference or other concerns, experimental units are coarse. `Region-split' experiments on online platforms are one example of such a setting. The cost, or regret, of experimentation is a natural concern here. Our new design, dubbed Synthetically Controlled Thompson Sampling (SCTS), minimizes the regret associated with experimentation at no practically meaningful loss to inferential ability. We provide theoretical guarantees characterizing the near-optimal regret of our approach, and the error rates achieved by the corresponding treatment effect estimator. Experiments on synthetic and real world data highlight the merits of our approach relative to both fixed and `switchback' designs common to such experimental settings.