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

We prove that the governing dynamics of a class of stochastic nonlinear networks can be learned through their coupling functions. 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 approach is plausible in numerous applications when one prefers to run an experiment only once but for a more extended period rather than repeating the same experiment multiple times under 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 actual coupling function. Extensive simulation results support our theoretical findings.