# Dissipative Gradient Descent Ascent Method: A Control Theory Inspired Algorithm for Min-max Optimization

arXiv: https://arxiv.org/abs/2403.09090 · HTML: https://mlsanity.com/paper/2403.09090/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 51 references that are in the map.
- First posted on arXiv 14 Mar 2024.

## Builds on (most cited first, 27 of 27)

- [Training GANs with Optimism](https://mlsanity.com/paper/1711.00141/) (2017)
- [A Variational Inequality Perspective on Generative Adversarial Networks](https://mlsanity.com/paper/1802.10551/) (2018)
- [A Unified Analysis of Extra-gradient and Optimistic Gradient Methods for Saddle Point Problems: Proximal Point Approach](https://mlsanity.com/paper/1901.08511/) (2019)
- [Near-Optimal Algorithms for Minimax Optimization](https://mlsanity.com/paper/2002.02417/) (2020)
- [Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints](https://mlsanity.com/paper/1408.3595/) (2014)
- [Interaction Matters: A Note on Non-asymptotic Local Convergence of Generative Adversarial Networks](https://mlsanity.com/paper/1802.06132/) (2018)
- [A Single-Loop Smoothed Gradient Descent-Ascent Algorithm for Nonconvex-Concave Min-Max Problems](https://mlsanity.com/paper/2010.15768/) (2020)
- [A Unified Single-loop Alternating Gradient Projection Algorithm for Nonconvex-Concave and Convex-Nonconcave Minimax Problems](https://mlsanity.com/paper/2006.02032/) (2020)
- [Banach Wasserstein GAN](https://mlsanity.com/paper/1806.06621/) (2018)
- [Connecting Generative Adversarial Networks and Actor-Critic Methods](https://mlsanity.com/paper/1610.01945/) (2016)
- [Faster Single-loop Algorithms for Minimax Optimization without Strong Concavity](https://mlsanity.com/paper/2112.05604/) (2021)
- [Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity](https://mlsanity.com/paper/2107.00052/) (2021)
- [Accelerated Zeroth-Order and First-Order Momentum Methods from Mini to Minimax Optimization](https://mlsanity.com/paper/2008.08170/) (2020)
- [Stochastic Gradient Descent-Ascent: Unified Theory and New Efficient Methods](https://mlsanity.com/paper/2202.07262/) (2022)
- [Stochastic Extragradient: General Analysis and Improved Rates](https://mlsanity.com/paper/2111.08611/) (2021)
- [Last-Iterate Convergent Policy Gradient Primal-Dual Methods for Constrained MDPs](https://mlsanity.com/paper/2306.11700/) (2023)
- [Dissipativity Theory for Nesterov's Accelerated Method](https://mlsanity.com/paper/1706.04381/) (2017)
- [Analysis of Optimization Algorithms via Integral Quadratic Constraints: Nonstrongly Convex Problems](https://mlsanity.com/paper/1705.03615/) (2017)
- [A Proximal Alternating Direction Method of Multiplier for Linearly Constrained Nonconvex Minimization](https://mlsanity.com/paper/1812.10229/) (2018)
- [Convergence of Gradient Methods on Bilinear Zero-Sum Games](https://mlsanity.com/paper/1908.05699/) (2019)
- [Universal Gradient Descent Ascent Method for Nonconvex-Nonconcave Minimax Optimization](https://mlsanity.com/paper/2212.12978/) (2022)
- [Smooth Monotone Stochastic Variational Inequalities and Saddle Point Problems: A Survey](https://mlsanity.com/paper/2208.13592/) (2022)
- [A Unified Analysis of First-Order Methods for Smooth Games via Integral Quadratic Constraints](https://mlsanity.com/paper/2009.11359/) (2020)
- [Discretized Distributed Optimization over Dynamic Digraphs](https://mlsanity.com/paper/2311.07939/) (2023)
- [Constrained Reinforcement Learning via Dissipative Saddle Flow Dynamics](https://mlsanity.com/paper/2212.01505/) (2022)
- [An integral quadratic constraint framework for real-time steady-state optimization of linear time-invariant systems](https://mlsanity.com/paper/1710.10204/) (2017)
- [Saddle Flow Dynamics: Observable Certificates and Separable Regularization](https://mlsanity.com/paper/2009.14714/) (2020)

## Built on by (most cited first, 4 of 4)

- [Multiplayer Federated Learning: Reaching Equilibrium with Less Communication](https://mlsanity.com/paper/2501.08263/) (2025)
- [Extragradient Method for (L0, L1)-Lipschitz Root-finding Problems](https://mlsanity.com/paper/2510.22421/) (2025)
- [Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization](https://mlsanity.com/paper/2604.05042/) (2026)
- [On Same-Sample and Independent-Sample Stochastic Extragradient for Monotone Variational Inequalities](https://mlsanity.com/paper/2608.06182/) (2026)

## Abstract (arXiv)

Gradient Descent Ascent (GDA) methods for min-max optimization problems typically produce oscillatory behavior that can lead to instability, e.g., in bilinear settings. To address this problem, we introduce a dissipation term into the GDA updates to dampen these oscillations. The proposed Dissipative GDA (DGDA) method can be seen as performing standard GDA on a state-augmented and regularized saddle function that does not strictly introduce additional convexity/concavity. We theoretically show the linear convergence of DGDA in the bilinear and strongly convex-strongly concave settings and assess its performance by comparing DGDA with other methods such as GDA, Extra-Gradient (EG), and Optimistic GDA. Our findings demonstrate that DGDA surpasses these methods, achieving superior convergence rates. We support our claims with two numerical examples that showcase DGDA's effectiveness in solving saddle point problems.