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We propose an alternating optimization algorithm to the nonconvex Koopmanoperator learning problem for nonlinear dynamic systems. We show that theproposed algorithm will converge to a critical point with rate $O(1/T)$ and$O(\frac{1}{\log T})$ for the constant and diminishing learning rates,respectively, under some mild conditions. To cope with the high dimensionalnonlinear dynamical systems, we present the first-ever distributed Koopmanoperator learning algorithm. We show that the distributed Koopman operatorlearning has the same convergence properties as the centralized Koopmanoperator learning, in the absence of optimal tracker, so long as the basisfunctions satisfy a set of state-based decomposition conditions. Numericalexperiments are provided to complement our theoretical results.

Towards Scalable Koopman Operator Learning: Convergence Rates and A Distributed Learning Algorithm