Comments on Efficient Singular Value Thresholding Computation

TL;DR

This paper presents a unified and efficient method for computing the proximal operator of convex functions of the nuclear norm, a key step in various low-rank matrix and tensor optimization algorithms.

Contribution

It introduces a general, unified approach for evaluating the proximal operator of convex functions of the nuclear norm, applicable across multiple applications.

Findings

Provides a computationally efficient procedure for the proximal operator

Unifies various case-specific solutions into a single framework

Facilitates faster optimization in low-rank matrix and tensor problems

Abstract

We discuss how to evaluate the proximal operator of a convex and increasing function of a nuclear norm, which forms the key computational step in several first-order optimization algorithms such as (accelerated) proximal gradient descent and ADMM. Various special cases of the problem arise in low-rank matrix completion, dropout training in deep learning and high-order low-rank tensor recovery, although they have all been solved on a case-by-case basis. We provide an unified and efficiently computable procedure for solving this problem.