# Differentially Private Empirical Risk Minimization with Input Perturbation

arXiv: https://arxiv.org/abs/1710.07425 · HTML: https://mlsanity.com/paper/1710.07425/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2017.

## Built on by (most cited first, 19 of 19)

- [Do Not Let Privacy Overbill Utility: Gradient Embedding Perturbation for Private Learning](https://mlsanity.com/paper/2102.12677/) (2021)
- [Private Convex Optimization via Exponential Mechanism](https://mlsanity.com/paper/2203.00263/) (2022)
- [When Does Differentially Private Learning Not Suffer in High Dimensions?](https://mlsanity.com/paper/2207.00160/) (2022)
- [Private Non-smooth Empirical Risk Minimization and Stochastic Convex Optimization in Subquadratic Steps](https://mlsanity.com/paper/2103.15352/) (2021)
- [ReSQueing Parallel and Private Stochastic Convex Optimization](https://mlsanity.com/paper/2301.00457/) (2023)
- [Differentially Private Federated Learning via Inexact ADMM](https://mlsanity.com/paper/2106.06127/) (2021)
- [DP-UTIL: Comprehensive Utility Analysis of Differential Privacy in Machine Learning](https://mlsanity.com/paper/2112.12998/) (2021)
- [Federated and Privacy-Preserving Learning of Accounting Data in Financial Statement Audits](https://mlsanity.com/paper/2208.12708/) (2022)
- [Evaluating Privacy-Preserving Machine Learning in Critical Infrastructures: A Case Study on Time-Series Classification](https://mlsanity.com/paper/2111.14838/) (2021)
- [MIAShield: Defending Membership Inference Attacks via Preemptive Exclusion of Members](https://mlsanity.com/paper/2203.00915/) (2022)
- [Differentially Private Learners for Heterogeneous Treatment Effects](https://mlsanity.com/paper/2503.03486/) (2025)
- [Purifying Approximate Differential Privacy with Randomized Post-processing](https://mlsanity.com/paper/2503.21071/) (2025)
- [DP-CDA: An Algorithm for Enhanced Privacy Preservation in Dataset Synthesis Through Randomized Mixing](https://mlsanity.com/paper/2411.16121/) (2024)
- [Online Linear Regression with Paid Stochastic Features](https://mlsanity.com/paper/2511.08073/) (2025)
- [Quadratic Objective Perturbation: Curvature-Based Differential Privacy](https://mlsanity.com/paper/2605.05905/) (2026)
- [Differentially Private Federated Learning via Inexact ADMM with Multiple Local Updates](https://mlsanity.com/paper/2202.09409/) (2022)
- [Does Privacy Always Harm Fairness? Data-Dependent Trade-offs via Chernoff Information Neural Estimation](https://mlsanity.com/paper/2601.13698/) (2026)
- [A Constrained Optimization Perspective of Unrolled Transformers](https://mlsanity.com/paper/2601.17257/) (2026)
- [An exponential mechanism based on quadratic approximations for fine-tuning machine learning models with privacy guarantees](https://mlsanity.com/paper/2605.20521/) (2026)

## Abstract (arXiv)

We propose a novel framework for the differentially private ERM, input perturbation. Existing differentially private ERM implicitly assumed that the data contributors submit their private data to a database expecting that the database invokes a differentially private mechanism for publication of the learned model. In input perturbation, each data contributor independently randomizes her/his data by itself and submits the perturbed data to the database. We show that the input perturbation framework theoretically guarantees that the model learned with the randomized data eventually satisfies differential privacy with the prescribed privacy parameters. At the same time, input perturbation guarantees that local differential privacy is guaranteed to the server. We also show that the excess risk bound of the model learned with input perturbation is O(1/n) under a certain condition, where n is the sample size. This is the same as the excess risk bound of the state-of-the-art.