Tensor Network Estimation of Distribution Algorithms

TL;DR

This paper explores tensor network-based generative models within evolutionary algorithms, revealing that model quality does not directly correlate with optimization success and that explicit mutation can enhance performance.

Contribution

It provides a new perspective on tensor network EDAs, highlighting the importance of mutation operators over generative model power.

Findings

Better generative models do not always lead to better optimization performance.

Adding explicit mutation operators can improve tensor network-based EDAs.

Optimization performance is not straightforwardly related to the generative model's quality.

Abstract

Tensor networks are a tool first employed in the context of many-body quantum physics that now have a wide range of uses across the computational sciences, from numerical methods to machine learning. Methods integrating tensor networks into evolutionary optimization algorithms have appeared in the recent literature. In essence, these methods can be understood as replacing the traditional crossover operation of a genetic algorithm with a tensor network-based generative model. We investigate these methods from the point of view that they are Estimation of Distribution Algorithms (EDAs). We find that optimization performance of these methods is not related to the power of the generative model in a straightforward way. Generative models that are better (in the sense that they better model the distribution from which their training data is drawn) do not necessarily result in better performance of the optimization algorithm they form a part of. This raises the question of how best to incorporate powerful generative models into optimization routines. In light of this we find that adding an explicit mutation operator to the output of the generative model often improves optimization performance.