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

TL;DR

This paper demonstrates that in certain stochastic dynamical networks, the coupling function governing the dynamics can be accurately learned from a single long trajectory, leveraging ergodic properties and concentration inequalities.

Contribution

It introduces a method to learn the coupling function of stochastic networks from only one sample trajectory, supported by theoretical convergence guarantees.

Findings

Coupling functions can be learned from a single trajectory.

Theoretical convergence results are established for the estimator.

Simulation results validate the approach.

Abstract

We consider a class of stochastic dynamical networks whose governing dynamics can be modeled using a coupling function. It is shown that the dynamics of such networks can generate geometrically ergodic trajectories under some reasonable assumptions. We show that a general class of coupling functions can be learned using only one sample trajectory from the network. This is practically plausible as in numerous applications it is desired to run an experiment only once but for a longer period of time, rather than repeating the same experiment multiple times from different initial conditions. Building upon ideas from the concentration inequalities for geometrically ergodic Markov chains, we formulate several results about the convergence of the empirical estimator to the true coupling function. Our theoretical findings are supported by extensive simulation results.