Learning Nonlinear Couplings in Network of Agents From a Single Sample Trajectory

In this article, we study a class of stochastic nonlinear dynamical networks governed by coupling functions, showing that under certain assumptions, these networks can produce geometrically ergodic trajectories. Our findings suggest that a wide range of coupling functions can be effectively learned from just one sample trajectory in the network. This approach is practical, as it often aligns with the preference in many applications to conduct a single, extended experiment rather than repeating the same experiment under different initial conditions. Drawing on concentration inequalities for geometrically ergodic Markov chains, we present several results regarding the empirical estimator's convergence to the actual coupling function, substantiated by extensive simulations.