Research map / Optimization / Nonconvex and smooth optimization
Extragradient for variational inequalities
Develops extragradient and optimistic methods for monotone and nonmonotone variational inequalities.
35 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2019–2026) · 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.
14 papers in 2023–24 and 8 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 4.4% to 2.3%.
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
- 2019 · On the convergence of single-call stochastic extra-gradient methods (NeurIPS 2019 · 23 citations)
- 2021 · Linear Last-iterate Convergence in Constrained Saddle-point Optimization (ICLR 2021 · 24 citations)
- 2022 · Optimal Algorithms for Decentralized Stochastic Variational Inequalities (NeurIPS 2022 · 9 citations)
- 2023 · Accelerated Single-Call Methods for Constrained Min-Max Optimization (ICLR 2023 · 3 citations)
- 2024 · Two-timescale Extragradient for Finding Local Minimax Points (ICLR 2024 · 1 citation)
- 2025 · Fast Zeroth-Order Convex Optimization with Quantum Gradient Methods (NeurIPS 2025 · 0 citations)
- 2026 · Accelerated and Stable Convergence with Anchored Generalized Optimistic Method (ICML 2026 · 0 citations)
Earliest papers here
- On the convergence of single-call stochastic extra-gradient methods (NeurIPS 2019 · 23 citations)
- An adaptive Mirror-Prox method for variational inequalities with singular operators (NeurIPS 2019)
- Linear Last-iterate Convergence in Constrained Saddle-point Optimization (ICLR 2021 · 24 citations)
What has been tried
25 papers here report 139 measured changes (a component added, removed or swapped, compared with a baseline): helped 62%, no clear effect 5%, hurt 28%, mixed 5%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Add anchoring to flip-flop-shuffled same-sample SEG | Convex-concave finite-sum minimax · minimum expected squared gradient norm | \Omega(1) -> \tilde{\gO}(\frac{1}{K^{1/3}}) | Helped | Stochastic Extragradient with Flip-Flop Shuffling & Anchoring: Provable Improvements (NeurIPS 2024 · 0 citations) |
| increase timescale separation from τ = 2 to τ = 20 | f(x,y) = -x² + 2xy · convergence to the local minimax point | Helped | Double-Step Alternating Extragradient with Increasing Timescale Separation for Finding Local Minimax Points: Provable Improvements (ICML 2024) |
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 22 papers; from OpenAlex and the papers' affiliations).
- Korea Advanced Institute of Science and Technology · 4 papers
- Yale University · 3 papers
- Mila · 3 papers
- University of California, Los Angeles · 2 papers
- University of California, Berkeley · 2 papers
- Mohamed bin Zayed University of Artificial Intelligence · 2 papers
- Meta · 2 papers
Use it
Download BibTeX of 32 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)
- Gradient descent ascent for minimax (31 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).