mlsanityData to 14 Oct 2026

A unified stochastic approximation framework for learning in games

arXiv 2206.03922 ↗First posted 8 Jun 2022cs.GT cs.LG math.OCcited by 23

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Abstract (arXiv)

We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms, including gradient-based methods, the exponential/multiplicative weights algorithm for learning in finite games, optimistic and bandit variants of the above, etc. In addition to providing an integrated view of these algorithms, our framework further allows us to obtain several new convergence results, both asymptotic and in finite time, in both continuous and finite games. Specifically, we provide a range of criteria for identifying classes of Nash equilibria and sets of action profiles that are attracting with high probability, and we also introduce the notion of coherence, a game-theoretic property that includes strict and sharp equilibria, and which leads to convergence in finite time. Importantly, our analysis applies to both oracle-based and bandit, payoff-based methods - that is, when players only observe their realized payoffs.

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). Builds on 19 of its 73 references that are in the map. First posted on arXiv 8 Jun 2022.

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19 of 73 references.

References · 19

  1. 2017Training GANs with Optimismcited by 217
  2. 2013Optimization, Learning, and Games with Predictable Sequencescited by 188
  3. 2015Fast Convergence of Regularized Learning in Gamescited by 150
  4. 2018A Variational Inequality Perspective on Generative Adversarial Networkscited by 144
  5. 2018Optimistic mirror descent in saddle-point problems: Going the extra (gradient) milecited by 136
  6. 2017Cycles in adversarial regularized learningcited by 124
  7. 2018Last-Iterate Convergence: Zero-Sum Games and Constrained Min-Max Optimizationcited by 98
  8. 2019On the convergence of single-call stochastic extra-gradient methodscited by 89
  9. 2016Learning in games with continuous action sets and unknown payoff functionscited by 81
  10. 2020On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problemscited by 80
  11. 2020The limits of min-max optimization algorithms: convergence to spurious non-critical setscited by 50
  12. 2020No-regret learning and mixed Nash equilibria: They do not mixcited by 50
7 more
  1. 2020Explore Aggressively, Update Conservatively: Stochastic Extragradient Methods with Variable Stepsize Scalingcited by 49
  2. 2018Bandit learning in concave N-person gamescited by 35
  3. 2014On the Characterization of Local Nash Equilibria in Continuous Gamescited by 22
  4. 2018Multi-agent online learning in time-varying gamescited by 17
  5. 2019Learning Nash Equilibria in Monotone Gamescited by 11
  6. 2018Learning with minimal information in continuous gamescited by 8
  7. 2017Learning Generalized Nash Equilibria in a Class of Convex Gamescited by 4

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Citing papers per year: 2023: 5; 2024: 4; 2025: 9; 2026: 5.

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  1. 2025Flow Density Control: Generative Optimization Beyond Entropy-Regularized Fine-Tuningcited by 17
  2. 2025Provable Maximum Entropy Manifold Exploration via Diffusion Modelscited by 14
  3. 2023Riemannian stochastic optimization methods avoid strict saddle pointscited by 8
  4. 2026Verifier-Constrained Flow Expansion for Discovery Beyond the Datacited by 7
  5. 2025Multiplayer Federated Learning: Reaching Equilibrium with Less Communicationcited by 5
  6. 2024No-regret learning in harmonic games: Extrapolation in the face of conflicting interestscited by 4
  7. 2023Exploiting hidden structures in non-convex games for convergence to Nash equilibriumcited by 3
  8. 2023Last-Iterate Convergence of Adaptive Riemannian Gradient Descent for Equilibrium Computationcited by 2
  9. 2023Payoff-based learning with matrix multiplicative weights in quantum gamescited by 2
  10. 2024Accelerated regularized learning in finite N-person gamescited by 2
  11. 2025The impact of uncertainty on regularized learning in gamescited by 2
  12. 2026A Unified Density Operator View of Flow Control and Mergingcited by 2
11 more
  1. 2023Sinkhorn Flow: A Continuous-Time Framework for Understanding and Generalizing the Sinkhorn Algorithmcited by 1
  2. 2026Shuffling the Data, Stretching the Step-size: Sharper Bias in constant step-size SGDcited by 1
  3. 2026Non-Asymptotic Convergence of Stochastic Iterative Algorithms: A Lyapunov Frameworkcited by 1
  4. 2024A Payoff-Based Policy Gradient Method in Stochastic Games with Long-Run Average Payoffscited by 0
  5. 2024Nested replicator dynamics, nested logit choice, and similarity-based learningcited by 0
  6. 2025Optimistic Online Learning in Symmetric Cone Gamescited by 0
  7. 2025Nash Equilibria in Games with Playerwise Concave Coupling Constraints: Existence and Computationcited by 0
  8. 2025Multi-agent learning under uncertainty: Recurrence vs. concentrationcited by 0
  9. 2025Robust equilibria in continuous games: From strategic to dynamic robustnesscited by 0
  10. 2025Computing Pure-Strategy Nash Equilibria in a Two-Party Policy Competition: Existence and Algorithmic Approachescited by 0
  11. 2026Regret, equilibrium, and learning in games: A guided tourcited by 0