Learning Nonlinear Couplings in Network of Agents from a Single Sample Trajectory
This addresses the challenge of network inference in applications where experiments can only be run once, offering a method for learning dynamics without repeated trials.
The paper tackles the problem of learning nonlinear coupling functions in stochastic dynamical networks from a single sample trajectory, showing that this is feasible under geometric ergodicity assumptions and providing convergence results for the empirical estimator.
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.