Distributionally Robust Framework for Equilibrium Seeking Under Unknown Dynamics by Gaussian Process Regression

This article presents a novel model-free distributionally robust framework for a challenging equilibrium-seeking problem (ESP) under fully unknown coupled dynamics. We consider a scenario in the ESP where the state transitions of players are governed by an unknown coupled dynamic system, and each player aims to minimize its own cost function. By predicting the stochastic distribution of player states through Gaussian process regression, we propose a novel distributionally robust approximation (DRA) that transforms the complex ESP with unknown coupled dynamic system into a solvable distributionally robust optimization problem. The gradient of the DRA's objective function is quantified, ensuring solvability. The effectiveness of the proposed DRA framework is evaluated through a nonlinear system, demonstrating comparable performance to model-based methods without requiring any dynamic model.