# Regret Minimization for Causal Inference on Large Treatment Space

arXiv: https://arxiv.org/abs/2006.05616 · HTML: https://mlsanity.com/paper/2006.05616/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2020.

## Built on by (most cited first, 7 of 7)

- [Reliable Off-Policy Learning for Dosage Combinations](https://mlsanity.com/paper/2305.19742/) (2023)
- [A Survey of Deep Causal Models and Their Industrial Applications](https://mlsanity.com/paper/2209.08860/) (2022)
- [Treatment Effect Estimation for Optimal Decision-Making](https://mlsanity.com/paper/2505.13092/) (2025)
- [Grab the Reins of Crowds: Estimating the Effects of Crowd Movement Guidance Using Causal Inference](https://mlsanity.com/paper/2102.03980/) (2021)
- [Causal Inference with Complex Treatments: A Survey](https://mlsanity.com/paper/2407.14022/) (2024)
- [A Distributionally Robust Framework for Nuisance in Causal Effect Estimation](https://mlsanity.com/paper/2505.17717/) (2025)
- [Multi-treatment Effect Estimation from Biomedical Data](https://mlsanity.com/paper/2112.07574/) (2021)

## Abstract (arXiv)

Predicting which action (treatment) will lead to a better outcome is a central task in decision support systems. To build a prediction model in real situations, learning from biased observational data is a critical issue due to the lack of randomized controlled trial (RCT) data. To handle such biased observational data, recent efforts in causal inference and counterfactual machine learning have focused on debiased estimation of the potential outcomes on a binary action space and the difference between them, namely, the individual treatment effect. When it comes to a large action space (e.g., selecting an appropriate combination of medicines for a patient), however, the regression accuracy of the potential outcomes is no longer sufficient in practical terms to achieve a good decision-making performance. This is because the mean accuracy on the large action space does not guarantee the nonexistence of a single potential outcome misestimation that might mislead the whole decision. Our proposed loss minimizes a classification error of whether or not the action is relatively good for the individual target among all feasible actions, which further improves the decision-making performance, as we prove. We also propose a network architecture and a regularizer that extracts a debiased representation not only from the individual feature but also from the biased action for better generalization in large action spaces. Extensive experiments on synthetic and semi-synthetic datasets demonstrate the superiority of our method for large combinatorial action spaces.