# Optimal Individualized Treatment Rule for Combination Treatments Under Budget Constraints

arXiv: https://arxiv.org/abs/2303.11507 · HTML: https://mlsanity.com/paper/2303.11507/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2023.

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

- [Individualized Policy Evaluation and Learning under Clustered Network Interference](https://mlsanity.com/paper/2311.02467/) (2023)
- [Doubly Robust Fusion of Many Treatments for Policy Learning](https://mlsanity.com/paper/2505.08092/) (2025)
- [A Doubly Robust Machine Learning Approach for Disentangling Treatment Effect Heterogeneity with Functional Outcomes](https://mlsanity.com/paper/2602.11118/) (2026)
- [Towards Optimal Environmental Policies: Policy Learning under Arbitrary Bipartite Network Interference](https://mlsanity.com/paper/2410.08362/) (2024)
- [Neural Supervised Clustering for Learning Individualized Treatment Rules with Many Treatments](https://mlsanity.com/paper/2610.19104/) (2026)

## Abstract (arXiv)

The individualized treatment rule (ITR), which recommends an optimal treatment based on individual characteristics, has drawn considerable interest from many areas such as precision medicine, personalized education, and personalized marketing. Existing ITR estimation methods mainly adopt one of two or more treatments. However, a combination of multiple treatments could be more powerful in various areas. In this paper, we propose a novel Double Encoder Model (DEM) to estimate the individualized treatment rule for combination treatments. The proposed double encoder model is a nonparametric model which not only flexibly incorporates complex treatment effects and interaction effects among treatments, but also improves estimation efficiency via the parameter-sharing feature. In addition, we tailor the estimated ITR to budget constraints through a multi-choice knapsack formulation, which enhances our proposed method under restricted-resource scenarios. In theory, we provide the value reduction bound with or without budget constraints, and an improved convergence rate with respect to the number of treatments under the DEM. Our simulation studies show that the proposed method outperforms the existing ITR estimation in various settings. We also demonstrate the superior performance of the proposed method in PDX data that recommends optimal combination treatments to shrink the tumor size of the colorectal cancer.