Towards Constituting Mathematical Structures for Learning to Optimize

摘要：

Learning to Optimize (L2O) is a technique that employs machine learning to automatically learn an optimization algorithm from data. It has gained significant attention in recent years and has been successfully applied to various applications such as signal and image processing. A generic L2O approach parameterizes the iterative update rule and learns the update direction using a black-box network. While this approach is widely applicable, it may overfit and not generalize well to out-of-distribution test sets. To address this issue, we derive basic mathematical conditions that successful update rules commonly satisfy. As a result, we propose a novel L2O model with a mathematics-inspired structure that is applicable to a wide range of problems and generalizes well to out-of-distribution issues. Numerical simulations support our theoretical findings and show the superior empirical performance of the proposed L2O model.

主讲人简介：

Jialin Liu received B.S. degree in automation from Tsinghua University in 2015 and received the Ph.D. degree in applied mathematics at University of California, Los Angeles (UCLA) in 2020. He is currently a senior algorithm engineer at DAMO Academy, Alibaba Group US. His research interest lies in the intersection of optimization and machine learning, with a particular focus on developing and analyzing machine-learning-driven algorithms for solving various optimization problems, such as continuous and combinatorial optimization. He won ``Best Student Paper: Third Place'' at the 2017 International Conference on Image Processing (ICIP).