Research map / Optimization / Nonconvex and smooth optimization
Gradient descent ascent for minimax
Analyzes local convergence and generalization of gradient descent ascent in GAN-style minimax training.
31 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2018–2025) · an approach in Nonconvex and smooth optimization, keyword cluster “games · zero sum · player”
State History Tried Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
7 papers in 2023–24 and 1 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 2.2% to 0.3%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2018 · The Mechanics of n-Player Differentiable Games (ICML 2018 · 138 citations)
- 2019 · Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile (ICLR 2019 · 114 citations)
- 2020 · On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems (ICML 2020 · 183 citations)
- 2021 · Proximal Gradient Descent-Ascent: Variable Convergence under KŁ Geometry (ICLR 2021 · 8 citations)
- 2022 · Hidden Convexity of Wasserstein GANs: Interpretable Generative Models with Closed-Form Solutions (ICLR 2022 · 3 citations)
- 2023 · Universal Gradient Descent Ascent Method for Nonconvex-Nonconcave Minimax Optimization (NeurIPS 2023 · 2 citations)
- 2024 · Fundamental Benefit of Alternating Updates in Minimax Optimization (ICML 2024 · 0 citations)
- 2025 · Convergence of Mean-Field Langevin Stochastic Descent-Ascent for Distributional Minimax Optimization (ICML 2025)
Earliest papers here
- The Mechanics of n-Player Differentiable Games (ICML 2018 · 138 citations)
- Training GANs with Optimism (ICLR 2018 · 120 citations)
- The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization (NeurIPS 2018 · 15 citations)
What has been tried
24 papers here report 147 measured changes (a component added, removed or swapped, compared with a baseline): helped 69%, no clear effect 8%, hurt 14%, mixed 9%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Use average historical gradient norm for St instead of current gradient norm, exponential average, or a constant | Generalized smooth minimax · SFO complexity | O(κ3ϵ−4) -> ˜O(κ3ϵ−4) | Hurt | Delving into the Convergence of Generalized Smooth Minimax Optimization (ICML 2024) |
Recent preprints
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Who publishes on it
Institutions on the most papers of this approach since 2023 (of 8 papers; from OpenAlex and the papers' affiliations).
- Korea Advanced Institute of Science and Technology · 2 papers
- The Chinese University of Hong Kong · 2 papers
Use it
Download BibTeX of 24 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Equilibrium learning in zero-sum games (88 papers)
- Extragradient for variational inequalities (35 papers)
Elsewhere in the topic
- Adaptive first-order convex methods (190 papers)
- Coordinate and Adam convergence analysis (188 papers)
- Stochastic gradient last-iterate analysis (178 papers)
- Nonconvex minimax and constrained methods (100 papers)
- Stochastic convex optimization complexity (94 papers)
- Acceleration and Nesterov dynamics (91 papers)
- Stochastic variance reduction (86 papers)
- Complexity of nonconvex first-order methods (79 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).