Work

Inexact Proximal Gradient Methods for Non-Convex and Non-Smooth Optimization

Year: 2018

Type: conference-paper

Abstract: In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal operator is time-consuming, or the proximal operator does not have an analytic solution. However, existing inexact proximal gradient methods only consider convex problems. The knowledge of inexact proximal gradient methods in the non-convex setting is very limited. To address this challenge, in this paper, we first propose three inexact proximal gradient algorithms, including the basic version and Nesterov’s accelerated version. After that, we provide the theoretical analysis to the basic and Nesterov’s accelerated versions. The theoretical results show that our inexact proximal gradient algorithms can have the same convergence rates as the ones of exact proximal gradient algorithms in the non-convex setting. Finally, we show the applications of our inexact proximal gradient algorithms on three representative non-convex learning problems. Empirical results confirm the superiority of our new inexact proximal gradient algorithms.

Source: Proceedings of the AAAI Conference on Artificial Intelligence

DOI: 10.1609/aaai.v32i1.11802

Authors: Bin Gu, De Wang, Zhouyuan Huo, Heng Huang

Institutions: University of Pittsburgh, The University of Texas at Arlington

Language: English

Topic: Stochastic Gradient Optimization Techniques

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, National Institutes of Health