# AGDA+: Proximal Alternating Gradient Descent Ascent Method with a Nonmonotone Adaptive Step-Size Search for Nonconvex Minimax Problems

arXiv: https://arxiv.org/abs/2406.14371 · HTML: https://mlsanity.com/paper/2406.14371/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2024.

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

- [Anomaly Detection and Early Warning Mechanism for Intelligent Monitoring Systems in Multi-Cloud Environments Based on LLM](https://mlsanity.com/paper/2506.07407/) (2025)
- [Gradient Norm Regularization Second-Order Algorithms for Solving Nonconvex-Strongly Concave Minimax Problems](https://mlsanity.com/paper/2411.15769/) (2024)
- [An Intelligent Fault Self-Healing Mechanism for Cloud AI Systems via Integration of Large Language Models and Deep Reinforcement Learning](https://mlsanity.com/paper/2506.07411/) (2025)
- [Safe and Adaptive Cloud Healing: Verifying LLM-Generated Recovery Plans with a Neural-Symbolic World Model](https://mlsanity.com/paper/2607.01595/) (2026)

## Abstract (arXiv)

We consider double-regularized nonconvex-strongly concave (NCSC) minimax problems of the form (P):minx∈X maxy∈Yg(x)+f(x,y)-h(y), where g, h are closed convex, f is L-smooth in (x,y) and strongly concave in y. We propose a proximal alternating gradient descent ascent method AGDA+ that can adaptively choose nonmonotone primal-dual stepsizes to compute an approximate stationary point for (P) without requiring the knowledge of the global Lipschitz constant L and the concavity modulus μ. Using a nonmonotone step-size search (backtracking) scheme, AGDA+ stands out by its ability to exploit the local Lipschitz structure and eliminates the need for precise tuning of hyper-parameters. AGDA+ achieves the optimal iteration complexity of O(ε-2) and it is the first step-size search method for NCSC minimax problems that require only 3 calls to nabla f on average per backtracking iteration. The numerical experiments demonstrate its robustness and efficiency.