Equilibrium Learning in Unbounded Stochastic Games with Gaussian Transitions
Abstract
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.
Related
- PAC-Bayesian Bounds for Learning Partially Observed Stochastic Linear Time-Invariant State-Space Systems with Inputs and Sub-Gaussian Noise
- A global stochastic maximum principle for forward-backward stochastic control systems with quadratic convex generator and unbounded terminal condition
- Three quantitative central limit theorems for the unbounded excursion component of a Gaussian field
- Backward stochastic partial differential equations with unbounded random coefficients
- Wave equation with unbounded terms driven by a stochastic measure
BibTeX
@misc{mavroforas2026equilibrium,
title = {{Equilibrium Learning in Unbounded Stochastic Games with Gaussian Transitions}},
author = {Jonathan Anthony Mavroforas and Fred Roosta},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16149},
eprint = {2610.16149},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16149},
}
RIS
TY - UNPB
TI - Equilibrium Learning in Unbounded Stochastic Games with Gaussian Transitions
AU - Jonathan Anthony Mavroforas
AU - Fred Roosta
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16149
UR - https://arxiv.org/abs/2610.16149
AB - 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.
ER -