Differentiable Linearized ADMM

Abstract

Recently, a number of learning-based optimization methods that combine data-driven architectures with the classical optimization algorithms have been proposed and explored, showing superior empirical performance in solving various ill-posed inverse problems, but there is still a scarcity of rigorous analysis about the convergence behaviors of learning-based optimization. In particular, most existing analyses are specific to unconstrained problems but cannot apply to the more general cases where some variables of interest are subject to certain constraints. In this paper, we propose Differentiable Linearized ADMM (D-LADMM) for solving the problems with linear constraints. Specifically, D-LADMM is a K-layer LADMM inspired deep neural network, which is obtained by firstly introducing some learnable weights in the classical Linearized ADMM algorithm and then generalizing the proximal operator to some learnable activation function. Notably, we rigorously prove that there exist a set of learnable parameters for D-LADMM to generate globally converged solutions, and we show that those desired parameters can be attained by training D-LADMM in a proper way. To the best of our knowledge, we are the first to provide the convergence analysis for the learning-based optimization method on constrained problems.

Accepted by ICML2019

Cited by in corpus (14)

• A Review on Deep Learning in Medical Image Reconstruction
• Learning to Optimize: A Primer and A Benchmark
• Deep Comprehensive Correlation Mining for Image Clustering
• Tuning-free Plug-and-Play Proximal Algorithm for Inverse Imaging Problems
• Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction
• TFPnP: Tuning-free Plug-and-Play Proximal Algorithm with Applications to Inverse Imaging Problems
• Safeguarded Learned Convex Optimization
• Feasibility-based Fixed Point Networks
• A Design Space Study for LISTA and Beyond
• Toward Model Parallelism for Deep Neural Network based on Gradient-free ADMM Framework
• A Novel Learnable Gradient Descent Type Algorithm for Non-convex Non-smooth Inverse Problems
• Graph Denoising with Framelet Regularizer
• Learned Interpretable Residual Extragradient ISTA for Sparse Coding
• Investigating Customization Strategies and Convergence Behaviors of Task-specific ADMM