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Equilibrium Learning in Unbounded Stochastic Games with Gaussian Transitions

arXiv 2610.16149 ↗First posted 12 Oct 2026stat.ML cs.LGcited by 0

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Abstract (arXiv)

Learning equilibria from data is difficult when several decision makers interact indefinitely and the system state has no prescribed bounds. We examine discounted general-sum stochastic games with compact action sets and an unknown nonlinear drift observed through Gaussian transition noise. The proposed procedure uses a single uninterrupted trajectory to update Gaussian-process models of the drift and to solve successively refined finite games. We prove a perturbation result showing that stability of equilibrium selection, together with uniform KL accuracy of Gaussian transition models, is sufficient for regional uniform convergence of the induced values and approximate Nash behavior in the original game. The region specifies where the guarantees are evaluated; strategies and dynamics continue to act on the entire Euclidean state space. For GP estimators, simultaneous confidence bounds yield a rate controlled by posterior uncertainty, kernel information gain, and joint-state dimension. Numerical studies illustrate how kernel choice and dimension appear in the predicted convergence behavior.

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References · 17

  1. 2017Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environmentscited by 1,558
  2. 2021The Surprising Effectiveness of PPO in Cooperative, Multi-Agent Gamescited by 942
  3. 2017Counterfactual Multi-Agent Policy Gradientscited by 751
  4. 2019The StarCraft Multi-Agent Challengecited by 597
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  7. 2019QTRAN: Learning to Factorize with Transformation for Cooperative Multi-Agent Reinforcement Learningcited by 379
  8. 2017On Kernelized Multi-armed Banditscited by 352
  9. 2020Benchmarking Multi-Agent Deep Reinforcement Learning Algorithms in Cooperative Taskscited by 212
  10. 2020Information Theoretic Regret Bounds for Online Nonlinear Controlcited by 90
  11. 2020Efficient Model-Based Reinforcement Learning through Optimistic Policy Search and Planningcited by 86
  12. 2020Active Learning for Nonlinear System Identification with Guaranteescited by 80
5 more
  1. 2019On Online Learning in Kernelized Markov Decision Processescited by 35
  2. 2023Optimal Exploration for Model-Based RL in Nonlinear Systemscited by 18
  3. 2024NeoRL: Efficient Exploration for Nonepisodic RLcited by 4
  4. 2025No-Regret Thompson Sampling for Finite-Horizon Markov Decision Processes with Gaussian Processescited by 4
  5. 2024Existence of ε-Nash Equilibria in Nonzero-Sum and Zero-Sum Markov Games with Standard Borel Spaces via Finite Model Approximationscited by 1

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