Research map / Optimization / Nonconvex and smooth optimization
Equilibrium learning in zero-sum games
Proves last-iterate and no-regret convergence of gradient dynamics to Nash and minmax equilibria.
88 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2017–2026) · an approach in Nonconvex and smooth optimization, keyword cluster “games · zero sum · player”
State History Tried Checklist 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.
24 papers in 2023–24 and 26 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic held steady, from 7.5% to 7.4%.
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
- 2017 · Efficient Regret Minimization in Non-Convex Games (ICML 2017 · 37 citations)
- 2018 · Acceleration through Optimistic No-Regret Dynamics (NeurIPS 2018 · 17 citations)
- 2019 · Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods (NeurIPS 2019 · 138 citations)
- 2020 · On Solving Minimax Optimization Locally: A Follow-the-Ridge Approach (ICLR 2020 · 51 citations)
- 2021 · Learning While Playing in Mean-Field Games: Convergence and Optimality (ICML 2021 · 9 citations)
- 2022 · On Last-Iterate Convergence Beyond Zero-Sum Games (ICML 2022 · 6 citations)
- 2023 · A Unified Approach to Reinforcement Learning, Quantal Response Equilibria, and Two-Player Zero-Sum Games (ICLR 2023 · 6 citations)
- 2024 · Approximating Nash Equilibria in Normal-Form Games via Stochastic Optimization (ICLR 2024 · 2 citations)
- 2025 · Beyond Monotonicity: On the Convergence of Learning Algorithms in Standard Auction Games (AAAI 2025 · 2 citations)
- 2026 · Nash Equilibria in Games with Playerwise Concave Coupling Constraints: Existence and Computation (ICML 2026 · 0 citations)
Earliest papers here
- Efficient Regret Minimization in Non-Convex Games (ICML 2017 · 37 citations)
- Strongly-Typed Agents are Guaranteed to Interact Safely (ICML 2017 · 0 citations)
- Acceleration through Optimistic No-Regret Dynamics (NeurIPS 2018 · 17 citations)
What has been tried
60 papers here report 380 measured changes (a component added, removed or swapped, compared with a baseline): helped 65%, no clear effect 11%, hurt 18%, mixed 7%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| use warmstarting and a fixed number of LMO calls per iteration | Two-player Leduc poker and two-player Liar's Dice · Nash gap | Helped | Efficient Learning in Polyhedral Games via Best-Response Oracles (AAAI 2024 · 1 citation) | |
| Replace the negative entropy regularizer with a squared Euclidean regularizer | A_δ (2×2 zero-sum game) · last-iterate duality gap | at least c_2 | No clear effect | Fast Last-Iterate Convergence of Learning in Games Requires Forgetful Algorithms (NeurIPS 2024 · 1 citation) |
| Use B_t = t^4 instead of B_t = d·t^4 | Zero-sum polymatrix games, bandit feedback · last-iterate convergence rate | \Tilde{O}(d^{\frac{1}{5}}k^{-\frac{1}{5}}) -> \Tilde{O}(dk^{-\frac{1}{5}}) | Mixed | From Average-Iterate to Last-Iterate Convergence in Games: A Reduction and Its Applications (NeurIPS 2025 · 0 citations) |
| Use non-vanishing friction instead of zero friction | Single-player, two-action strict Nash game · strategy error decay rate | \sim \exp\parens*{\Const - \frac{\step^2\horizon^2}{2(\step\fr+1)}}; \sim \exp\parens*{\Const - \frac{\step}{\fr}\run} | Hurt | Accelerated Regularized Learning in Finite N-Person Games (NeurIPS 2024 · 0 citations) |
| Increase the number of sampled instances per iteration | Kuhn Poker and Liars Dice · duality gap | Helped | Reducing Variance of Stochastic Optimization for Approximating Nash Equilibria in Normal-Form Games (ICML 2025) |
What reviewers will expect
Datasets and baselines named in the 19 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Baselines
- fictitious play · 2 of 19 papers
- accelerated optimistic gradient · 2 of 19 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 50 papers; from OpenAlex and the papers' affiliations).
- Yale University · 6 papers
- Google DeepMind · 5 papers
- Singapore University of Technology and Design · 5 papers
- Massachusetts Institute of Technology · 4 papers
- Columbia University · 4 papers
- University of California, Irvine · 4 papers
- University of Wisconsin - Madison · 4 papers
- Stanford University · 3 papers
- EPFL · 3 papers
- Nanjing University · 3 papers
Use it
Download BibTeX of 40 key papersOpen the topic in the interactive map
Get alerts. Describe your idea in scime atlas and save it (free scime account): you get a weekly email when new preprints land close to it.
Related approaches
Same keyword cluster
- Extragradient for variational inequalities (35 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).