mlsanityData to 7 Oct 2026

Learning in games with continuous action sets and unknown payoff functions

arXiv 1608.07310 ↗First posted 25 Aug 2016math.OC cs.GT cs.LGcited by 78

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Abstract (arXiv)

This paper examines the convergence of no-regret learning in games with continuous action sets. For concreteness, we focus on learning via "dual averaging", a widely used class of no-regret learning schemes where players take small steps along their individual payoff gradients and then "mirror" the output back to their action sets. In terms of feedback, we assume that players can only estimate their payoff gradients up to a zero-mean error with bounded variance. To study the convergence of the induced sequence of play, we introduce the notion of variational stability, and we show that stable equilibria are locally attracting with high probability whereas globally stable equilibria are globally attracting with probability 1. We also discuss some applications to mixed-strategy learning in finite games, and we provide explicit estimates of the method's convergence speed.

Key facts. Cited by 78 papers in the map (data through 7 Oct 2026). First posted on arXiv 25 Aug 2016.

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Citing papers per year: 2021: 17; 2022: 17; 2023: 18; 2024: 10; 2025: 11; 2026: 5.

78 papers.

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  1. 2021Decentralized Q-Learning in Zero-sum Markov Gamescited by 53
  2. 2021Adaptive Learning in Continuous Games: Optimal Regret Bounds and Convergence to Nash Equilibriumcited by 51
  3. 2021Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivitycited by 43
  4. 2022Multiplayer Performative Prediction: Learning in Decision-Dependent Gamescited by 42
  5. 2022Stochastic Gradient Descent-Ascent: Unified Theory and New Efficient Methodscited by 37
  6. 2021Stochastic Extragradient: General Analysis and Improved Ratescited by 31
  7. 2021The Confluence of Networks, Games and Learningcited by 26
  8. 2021Beyond Exact Gradients: Convergence of Stochastic Soft-Max Policy Gradient Methods with Entropy Regularizationcited by 25
  9. 2022Near-Optimal No-Regret Learning Dynamics for General Convex Gamescited by 25
  10. 2021Survival of the strictest: Stable and unstable equilibria under regularized learning with partial informationcited by 22
  11. 2022A unified stochastic approximation framework for learning in gamescited by 22
  12. 2024Magnetic Preference Optimization: Achieving Last-iterate Convergence for Language Model Alignmentcited by 20
38 more
  1. 2022No-Regret Learning in Games with Noisy Feedback: Faster Rates and Adaptivity via Learning Rate Separationcited by 17
  2. 2021Doubly Optimal No-Regret Online Learning in Strongly Monotone Games with Bandit Feedbackcited by 14
  3. 2023Single-Call Stochastic Extragradient Methods for Structured Non-monotone Variational Inequalities: Improved Analysis under Weaker Conditionscited by 14
  4. 2022Clipped Stochastic Methods for Variational Inequalities with Heavy-Tailed Noisecited by 13
  5. 2022On the convergence of policy gradient methods to Nash equilibria in general stochastic gamescited by 13
  6. 2021The Last-Iterate Convergence Rate of Optimistic Mirror Descent in Stochastic Variational Inequalitiescited by 12
  7. 2023Doubly Optimal No-Regret Learning in Monotone Gamescited by 12
  8. 2023Mastering Strategy Card Game (Legends of Code and Magic) via End-to-End Policy and Optimistic Smooth Fictitious Playcited by 10
  9. 2023Mastering Strategy Card Game (Hearthstone) with Improved Techniquescited by 10
  10. 2021Follow-the-Regularized-Leader Routes to Chaos in Routing Gamescited by 9
  11. 2022First-Order Algorithms for Nonlinear Generalized Nash Equilibrium Problemscited by 9
  12. 2022Last-Iterate Convergence with Full and Noisy Feedback in Two-Player Zero-Sum Gamescited by 9
  13. 2023Adaptively Perturbed Mirror Descent for Learning in Gamescited by 9
  14. 2025Instance-Dependent Regret Bounds for Learning Two-Player Zero-Sum Games with Bandit Feedbackcited by 9
  15. 2021Inducing Equilibria via Incentives: Simultaneous Design-and-Play Ensures Global Convergencecited by 8
  16. 2023Partially Personalized Federated Learning: Breaking the Curse of Data Heterogeneitycited by 8
  17. 2021Learning in nonatomic games, Part I: Finite action spaces and population gamescited by 6
  18. 2022Learning Stationary Nash Equilibrium Policies in n-Player Stochastic Games with Independent Chainscited by 6
  19. 2023Asymptotic Convergence and Performance of Multi-Agent Q-Learning Dynamicscited by 6
  20. 2023Stochastic Methods in Variational Inequalities: Ergodicity, Bias and Refinementscited by 6
  21. 2023Adaptive, Doubly Optimal No-Regret Learning in Strongly Monotone and Exp-Concave Games with Gradient Feedbackcited by 6
  22. 2022Perseus: A Simple and Optimal High-Order Method for Variational Inequalitiescited by 5
  23. 2025Multiplayer Federated Learning: Reaching Equilibrium with Less Communicationcited by 5
  24. 2025Expected Variational Inequalitiescited by 5
  25. 2021Adaptive first-order methods revisited: Convex optimization without Lipschitz requirementscited by 4
  26. 2022Differentiable Bilevel Programming for Stackelberg Congestion Gamescited by 4
  27. 2023Learning in quantum gamescited by 4
  28. 2023The equivalence of dynamic and strategic stability under regularized learning in gamescited by 4
  29. 2024A geometric decomposition of finite games: Convergence vs. recurrence under exponential weightscited by 4
  30. 2024Learning to Control Unknown Strongly Monotone Gamescited by 4
  31. 2024No-regret learning in harmonic games: Extrapolation in the face of conflicting interestscited by 4
  32. 2021Distributed stochastic optimization with large delayscited by 3
  33. 2024Understanding Model Selection For Learning In Strategic Environmentscited by 3
  34. 2024Proximal Point Method for Online Saddle Point Problemcited by 3
  35. 2023Last-Iterate Convergence of Adaptive Riemannian Gradient Descent for Equilibrium Computationcited by 2
  36. 2023Payoff-based learning with matrix multiplicative weights in quantum gamescited by 2
  37. 2023Exploiting hidden structures in non-convex games for convergence to Nash equilibriumcited by 2
  38. 2024Decentralized and Uncoordinated Learning of Stable Matchings: A Game-Theoretic Approachcited by 2

50 most cited of 78 All 78 (JSON)