mlsanityData to 7 Oct 2026

Second-Order Mirror Descent: Convergence in Games Beyond Averaging and Discounting

arXiv 2111.09982 ↗First posted 18 Nov 2021math.OC cs.GT cs.LGcited by 1

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Abstract (arXiv)

In this paper, we propose a second-order extension of the continuous-time game-theoretic mirror descent (MD) dynamics, referred to as MD2, which provably converges to mere (but not necessarily strict) variationally stable states (VSS) without using common auxiliary techniques such as time-averaging or discounting. We show that MD2 enjoys no-regret as well as an exponential rate of convergence towards strong VSS upon a slight modification. MD2 can also be used to derive many novel continuous-time primal-space dynamics. We then use stochastic approximation techniques to provide a convergence guarantee of discrete-time MD2 with noisy observations towards interior mere VSS. Selected simulations are provided to illustrate our results.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 16 of its 81 references that are in the map. First posted on arXiv 18 Nov 2021.

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16 of 81 references.

References · 16

  1. 2017Training GANs with Optimismcited by 217
  2. 2017Cycles in adversarial regularized learningcited by 122
  3. 2016Learning in games with continuous action sets and unknown payoff functionscited by 78
  4. 2020No-regret learning and mixed Nash equilibria: They do not mixcited by 49
  5. 2018On Gradient-Based Learning in Continuous Gamescited by 46
  6. 2019Exponentiated Gradient Meets Gradient Descentcited by 32
  7. 2019First-order optimization algorithms via inertial systems with Hessian driven dampingcited by 22
  8. 2021Survival of the strictest: Stable and unstable equilibria under regularized learning with partial informationcited by 22
  9. 2019Learning Nash Equilibria in Monotone Gamescited by 10
  10. 2015Finite composite games: Equilibria and dynamicscited by 8
  11. 2018On Passivity, Reinforcement Learning and Higher-Order Learning in Multi-Agent Finite Gamescited by 8
  12. 2018Convergence of the Iterates in Mirror Descent Methodscited by 7
4 more
  1. 2018Learning with minimal information in continuous gamescited by 7
  2. 2019Continuous-time Discounted Mirror-Descent Dynamics in Monotone Concave Gamescited by 4
  3. 2019RLC Circuits based Distributed Mirror Descent Methodcited by 2
  4. 2020Continuous-Time Convergence Rates in Potential and Monotone Gamescited by 1

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Citing papers per year: 2024: 1.

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  1. 2024Accelerated regularized learning in finite N-person gamescited by 2