Algorithmic (Semi-)Conjugacy via Koopman Operator Theory

TL;DR

This paper introduces a spectral analysis framework based on Koopman operator theory to classify and compare iterative algorithms viewed as discrete dynamical systems, facilitating understanding of their relationships.

Contribution

It develops a novel method to identify (semi-)conjugacies between algorithms through spectral properties, enabling systematic classification and comparison.

Findings

Spectral properties reveal relationships between algorithms.

Framework applies to various iterative methods.

Provides a new perspective for algorithm analysis.

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.