Algorithmic (Semi-)Conjugacy via Koopman Operator Theory

William T. Redman, Maria Fonoberova, Ryan Mohr, Ioannis G. Kevrekidis, Igor Mezic

Abstract: Iterative algorithms are of utmost importance in decision and control. With an ever growing number of algorithms being developed, distributed, and proprietarized, there is a similarly growing need for methods that can provide classification and comparison. By viewing iterative algorithms as discrete-time dynamical systems, we leverage Koopman operator theory to identify (semi-)conjugacies between algorithms using their spectral properties. This provides a general framework with which to classify and compare algorithms.