Differentiable Linearized ADMM
Xingyu Xie · Jianlong Wu · Guangcan Liu · Zhisheng Zhong · Zhouchen Lin

Tue Jun 11th 04:20 -- 04:25 PM @ Hall B

Recently, a great many 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. However, there is still a scarcity of rigorous analysis about the convergence behaviors of learning-based optimization. In particular, most existing theories 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 mathematically 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 one to provide the convergence analysis for the learning-based optimization method on constrained problems. Experiments on simulative and real applications verify the superiorities of D-LADMM over LADMM.

Author Information

Xingyu Xie (Peking Unversity)
Jianlong Wu (Peking University)
Guangcan Liu (Nanjing University of Information Science and Technology)

He received the bachelor's degree in mathematics and the Ph.D. degree in computer science and engineering from Shanghai Jiao Tong University, Shanghai, China, in 2004 and 2010, respectively. He was a Post-Doctoral Researcher with the National University of Singapore, Singapore, from 2011 to 2012, the University of Illinois at Urbana-Champaign, Champaign, IL, USA, from 2012 to 2013, Cornell University, Ithaca, NY, USA, from 2013 to 2014, and Rutgers University, Piscataway, NJ, USA, in 2014. Since 2014, he has been a Professor with the School of Information and Control, Nanjing University of Information Science and Technology, Nanjing, China. His research interests touch on the areas of pattern recognition and signal processing. He is the recipient of the National Excellent Youth Fund 2016 and Clarivate Analytics Highly Cited Researcher 2017.

Zhisheng Zhong (Peking University)
Zhouchen Lin (Peking University)

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