Initialization Method for Factorization Machine Based on Low-Rank Approximation for Constructing a Corrected Approximate Ising Model

TL;DR

This paper introduces a low-rank approximation initialization method for factorization machines to improve the performance of quantum annealing in solving black-box combinatorial optimization problems.

Contribution

It proposes a novel low-rank approximation initialization technique for FMs and demonstrates its effectiveness for warm-starting FMQA in optimization tasks.

Findings

The low-rank approximation method improves initialization accuracy.

The method's effectiveness is consistent across different Ising models.

Numerical experiments confirm enhanced optimization performance.

Abstract

This paper presents an initialization method that can approximate a given approximate Ising model with a high degree of accuracy using a factorization machine (FM), a machine learning model. The construction of an Ising models using an FM is applied to black-box combinatorial optimization problems using factorization machine with quantum annealing (FMQA). It is anticipated that the optimization performance of FMQA will be enhanced through an implementation of the warm-start method. Nevertheless, the optimal initialization method for leveraging the warm-start approach in FMQA remains undetermined. Consequently, the present study compares initialization methods based on random initialization and low-rank approximation, and then identifies a suitable one for use with warm-start in FMQA through numerical experiments. Furthermore, the properties of the initialization method by the low-rank approximation for the FM are analyzed using random matrix theory, demonstrating that the approximation accuracy of the proposed method is not significantly influenced by the specific Ising model under consideration. The findings of this study will facilitate advancements of research in the field of black-box combinatorial optimization through the use of Ising machines.