# Equilibrium Learning in Unbounded Stochastic Games with Gaussian Transitions

arXiv: https://arxiv.org/abs/2610.16149 · HTML: https://mlsanity.com/paper/2610.16149/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 24 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 17 of 17)

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- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Benchmarking Multi-Agent Deep Reinforcement Learning Algorithms in Cooperative Tasks](https://mlsanity.com/paper/2006.07869/) (2020)
- [Information Theoretic Regret Bounds for Online Nonlinear Control](https://mlsanity.com/paper/2006.12466/) (2020)
- [Efficient Model-Based Reinforcement Learning through Optimistic Policy Search and Planning](https://mlsanity.com/paper/2006.08684/) (2020)
- [Active Learning for Nonlinear System Identification with Guarantees](https://mlsanity.com/paper/2006.10277/) (2020)
- [On Online Learning in Kernelized Markov Decision Processes](https://mlsanity.com/paper/1911.01871/) (2019)
- [Optimal Exploration for Model-Based RL in Nonlinear Systems](https://mlsanity.com/paper/2306.09210/) (2023)
- [NeoRL: Efficient Exploration for Nonepisodic RL](https://mlsanity.com/paper/2406.01175/) (2024)
- [No-Regret Thompson Sampling for Finite-Horizon Markov Decision Processes with Gaussian Processes](https://mlsanity.com/paper/2510.20725/) (2025)
- [Existence of ε-Nash Equilibria in Nonzero-Sum and Zero-Sum Markov Games with Standard Borel Spaces via Finite Model Approximations](https://mlsanity.com/paper/2411.10805/) (2024)

## 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.