# A Differentially Private Weighted Empirical Risk Minimization Procedure and its Application to Outcome Weighted Learning

arXiv: https://arxiv.org/abs/2307.13127 · HTML: https://mlsanity.com/paper/2307.13127/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 84 references that are in the map.
- First posted on arXiv 24 Jul 2023.

## Builds on (most cited first, 16 of 16)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Residual Weighted Learning for Estimating Individualized Treatment Rules](https://mlsanity.com/paper/1508.03179/) (2015)
- [Tight Lower Bounds for Differentially Private Selection](https://mlsanity.com/paper/1704.03024/) (2017)
- [On the (In)Feasibility of Attribute Inference Attacks on Machine Learning Models](https://mlsanity.com/paper/2103.07101/) (2021)
- [Finite-sample analysis of M-estimators using self-concordance](https://mlsanity.com/paper/1810.06838/) (2018)
- [Differentially Private Estimation of Heterogeneous Causal Effects](https://mlsanity.com/paper/2202.11043/) (2022)
- [Comparative Study of Differentially Private Data Synthesis Methods](https://mlsanity.com/paper/1602.01063/) (2016)
- [A New Perspective on Robust M-Estimation: Finite Sample Theory and Applications to Dependence-Adjusted Multiple Testing](https://mlsanity.com/paper/1711.05381/) (2017)
- [Statistical Properties of Sanitized Results from Differentially Private Laplace Mechanism with Univariate Bounding Constraints](https://mlsanity.com/paper/1607.08554/) (2016)
- [Model-based Differentially Private Data Synthesis and Statistical Inference in Multiply Synthetic Differentially Private Data](https://mlsanity.com/paper/1606.08052/) (2016)

## Built on by (most cited first, 3 of 3)

- [Differential Privacy Under Class Imbalance: Methods and Empirical Insights](https://mlsanity.com/paper/2411.05733/) (2024)
- [DPpack: An R Package for Differentially Private Statistical Analysis and Machine Learning](https://mlsanity.com/paper/2309.10965/) (2023)
- [Differentially Private Two-Stage Empirical Risk Minimization with Applications to Individualized Treatment Rule](https://mlsanity.com/paper/2602.12604/) (2026)

## Abstract (arXiv)

Data used to train predictive models via empirical risk minimization (ERM) often contain sensitive personal information. While differential privacy (DP) provides mathematically provable bounds to protect such data, previous work has focused almost exclusively on unweighted ERM. We consider weighted ERM (wERM) -- an important generalization where individual contributions to the objective function vary. We propose the first DP algorithm for general wERM with formal privacy guarantees and derive both its empirical and population utility bounds. Crucially, this general wERM framework provides a pathway for deriving privacy-preserving learning methods for individualized treatment rules, including the popular outcome-weighted learning (OWL) approach. We evaluate DP-wERM applied to OWL in simulated and real data experiments. Our empirical results demonstrate that training OWL models via wERM provides strong DP guarantees while maintaining robust performance, proving the method is practical for sensitive, real-world data.