# Differentially Private Two-Stage Empirical Risk Minimization with Applications to Individualized Treatment Rule

arXiv: https://arxiv.org/abs/2602.12604 · HTML: https://mlsanity.com/paper/2602.12604/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 45 references that are in the map.
- First posted on arXiv 13 Feb 2026.

## Builds on (most cited first, 17 of 17)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [Generalized Optimal Matching Methods for Causal Inference](https://mlsanity.com/paper/1612.08321/) (2016)
- [Minimal Dispersion Approximately Balancing Weights: Asymptotic Properties and Practical Considerations](https://mlsanity.com/paper/1705.00998/) (2017)
- [Benchmarking Heterogeneous Treatment Effect Models through the Lens of Interpretability](https://mlsanity.com/paper/2206.08363/) (2022)
- [Differentially Private Estimation of Heterogeneous Causal Effects](https://mlsanity.com/paper/2202.11043/) (2022)
- [Entropy balancing is doubly robust](https://mlsanity.com/paper/1501.03571/) (2015)
- [Energy Balancing of Covariate Distributions](https://mlsanity.com/paper/2004.13962/) (2020)
- [Differentially Private Covariate Balancing Causal Inference](https://mlsanity.com/paper/2410.14789/) (2024)
- [Differentially Private Estimation and Inference in High-Dimensional Regression with FDR Control](https://mlsanity.com/paper/2310.16260/) (2023)
- [Robust Sample Weighting to Facilitate Individualized Treatment Rule Learning for a Target Population](https://mlsanity.com/paper/2105.00581/) (2021)
- [A Differentially Private Weighted Empirical Risk Minimization Procedure and its Application to Outcome Weighted Learning](https://mlsanity.com/paper/2307.13127/) (2023)
- [Entropy Balancing for Causal Generalization with Target Sample Summary Information](https://mlsanity.com/paper/2201.08012/) (2022)
- [A reluctant additive model framework for interpretable nonlinear individualized treatment rules](https://mlsanity.com/paper/2311.01538/) (2023)
- [Statistical Inference for Differentially Private Stochastic Gradient Descent](https://mlsanity.com/paper/2507.20560/) (2025)
- [Stabilized Direct Learning for Efficient Estimation of Individualized Treatment Rules](https://mlsanity.com/paper/2112.03981/) (2021)

## Abstract (arXiv)

Differential privacy provides a formal framework for releasing statistical estimators that limit how much any single observation can influence the output, by injecting calibrated random noise. We study differentially private estimation in two-stage procedures common in causal inference and individualized treatment rule (ITR) learning, in which data-dependent weights are first estimated to enforce covariate balance and a parameter of interest is then obtained by weighted empirical risk minimization. We propose Differentially Private Two-Stage Empirical Risk Minimization (DP-2ERM), which privatizes the final estimator directly through objective perturbation calibrated to the data-dependent sensitivity of the full pipeline. The analysis combines deterministic weight-perturbation bounds for several covariate-balancing methods (inverse propensity weighting, entropy balancing weighting, and maximum mean discrepancy weighting) with probabilistic sensitivity bounds for the second-stage solution. The resulting calibration is sharper than the natural stage-wise composition baseline, which the same sensitivity analysis supplies as a byproduct. Simulation studies and a benchmark application to ITR learning demonstrate the improved privacy--utility trade-off.