Relaxation-assisted reverse annealing on nonnegative/binary matrix factorization

TL;DR

This paper introduces a novel approach combining reverse annealing with linear programming relaxation to improve quantum annealing performance in nonnegative/binary matrix factorization, demonstrating better convergence and optimization results.

Contribution

It proposes an integrated strategy that uses relaxed solutions as initial states for reverse annealing, enhancing optimization in matrix factorization tasks.

Findings

Improved convergence over existing reverse annealing methods.

Relaxation-based initialization correlates with optimal solutions.

Method achieves performance comparable to exact optimization.

Abstract

Quantum annealing has garnered significant attention as meta-heuristics inspired by quantum physics for combinatorial optimization problems. Among its many applications, nonnegative/binary matrix factorization stands out for its complexity and relevance in unsupervised machine learning. The use of reverse annealing, a derivative procedure of quantum annealing to prioritize the search in a vicinity under a given initial state, helps improve its optimization performance in matrix factorization. This study proposes an improved strategy that integrates reverse annealing with a linear programming relaxation technique. Using relaxed solutions as the initial configuration for reverse annealing, we demonstrate improvements in optimization performance comparable to the exact optimization methods. Our experiments on facial image datasets show that our method provides better convergence than known reverse annealing methods. Furthermore, we investigate the effectiveness of relaxation-based initialization methods on randomized datasets, demonstrating a relationship between the relaxed solution and the optimal solution. This research underscores the potential of combining reverse annealing and classical optimization strategies to enhance optimization performance.