# Enhancing Privacy in Decentralized Min-Max Optimization: A Differentially Private Approach

arXiv: https://arxiv.org/abs/2508.07505 · HTML: https://mlsanity.com/paper/2508.07505/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 49 of its 86 references that are in the map.
- First posted on arXiv 10 Aug 2025.

## Builds on (most cited first, 30 of 49)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [Local Model Poisoning Attacks to Byzantine-Robust Federated Learning](https://mlsanity.com/paper/1911.11815/) (2019)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [FLTrust: Byzantine-robust Federated Learning via Trust Bootstrapping](https://mlsanity.com/paper/2012.13995/) (2020)
- [Momentum-Based Variance Reduction in Non-Convex SGD](https://mlsanity.com/paper/1905.10018/) (2019)
- [SPIDER: Near-Optimal Non-Convex Optimization via Stochastic Path Integrated Differential Estimator](https://mlsanity.com/paper/1807.01695/) (2018)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Mime: Mimicking Centralized Stochastic Algorithms in Federated Learning](https://mlsanity.com/paper/2008.03606/) (2020)
- [Supervised Pretraining Can Learn In-Context Reinforcement Learning](https://mlsanity.com/paper/2306.14892/) (2023)
- [LDP-Fed: Federated Learning with Local Differential Privacy](https://mlsanity.com/paper/2006.03637/) (2020)
- [Differentially Private Empirical Risk Minimization Revisited: Faster and More General](https://mlsanity.com/paper/1802.05251/) (2018)
- [Near-Optimal Algorithms for Minimax Optimization](https://mlsanity.com/paper/2002.02417/) (2020)
- [Stochastic Recursive Gradient Descent Ascent for Stochastic Nonconvex-Strongly-Concave Minimax Problems](https://mlsanity.com/paper/2001.03724/) (2020)
- [Understanding Clipping for Federated Learning: Convergence and Client-Level Differential Privacy](https://mlsanity.com/paper/2106.13673/) (2021)
- [Byzantine-Robust Decentralized Federated Learning](https://mlsanity.com/paper/2406.10416/) (2024)
- [STEM: A Stochastic Two-Sided Momentum Algorithm Achieving Near-Optimal Sample and Communication Complexities for Federated Learning](https://mlsanity.com/paper/2106.10435/) (2021)
- [Stochastic Gradient Descent-Ascent: Unified Theory and New Efficient Methods](https://mlsanity.com/paper/2202.07262/) (2022)
- [Transformers are Minimax Optimal Nonparametric In-Context Learners](https://mlsanity.com/paper/2408.12186/) (2024)
- [Robust Multi-Agent Reinforcement Learning with State Uncertainty](https://mlsanity.com/paper/2307.16212/) (2023)
- [Source Inference Attacks in Federated Learning](https://mlsanity.com/paper/2109.05659/) (2021)
- [Muffliato: Peer-to-Peer Privacy Amplification for Decentralized Optimization and Averaging](https://mlsanity.com/paper/2206.05091/) (2022)
- [Differentially Private SGDA for Minimax Problems](https://mlsanity.com/paper/2201.09046/) (2022)
- [Bring Your Own Algorithm for Optimal Differentially Private Stochastic Minimax Optimization](https://mlsanity.com/paper/2206.00363/) (2022)
- [A Hybrid Variance-Reduced Method for Decentralized Stochastic Non-Convex Optimization](https://mlsanity.com/paper/2102.06752/) (2021)
- [Empirical Risk Minimization in Non-interactive Local Differential Privacy: Efficiency and High Dimensional Case](https://mlsanity.com/paper/1802.04085/) (2018)

## Abstract (arXiv)

Decentralized min-max optimization allows multi-agent systems to collaboratively solve global min-max optimization problems by facilitating the exchange of model updates among neighboring agents, eliminating the need for a central server. However, sharing model updates in such systems carry a risk of exposing sensitive data to inference attacks, raising significant privacy concerns. To mitigate these privacy risks, differential privacy (DP) has become a widely adopted technique for safeguarding individual data. Despite its advantages, implementing DP in decentralized min-max optimization poses challenges, as the added noise can hinder convergence, particularly in non-convex scenarios with complex agent interactions in min-max optimization problems. In this work, we propose an algorithm called DPMixSGD (Differential Private Minmax Hybrid Stochastic Gradient Descent), a novel privacy-preserving algorithm specifically designed for non-convex decentralized min-max optimization. Our method builds on the state-of-the-art STORM-based algorithm, one of the fastest decentralized min-max solutions. We rigorously prove that the noise added to local gradients does not significantly compromise convergence performance, and we provide theoretical bounds to ensure privacy guarantees. To validate our theoretical findings, we conduct extensive experiments across various tasks and models, demonstrating the effectiveness of our approach.