Towards Constituting Mathematical Structures for Learning to Optimize

• URL: http://arxiv.org/abs/2305.18577v1
• Date: Mon, 29 May 2023 19:37:28 GMT
• Title: Towards Constituting Mathematical Structures for Learning to Optimize
• Authors: Jialin Liu, Xiaohan Chen, Zhangyang Wang, Wotao Yin, HanQin Cai
• Abstract summary: A technique that utilizes machine learning to learn an optimization algorithm automatically from data has gained arising attention in recent years. A generic L2O approach parameterizes the iterative update rule and learns the update direction as a black-box network. While the generic approach is widely applicable, the learned model can overfit and may not generalize well to out-of-distribution test sets. We propose a novel L2O model with a mathematics-inspired structure that is broadly applicable and generalized well to out-of-distribution problems.
• Score: 101.80359461134087
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Learning to Optimize (L2O), a technique that utilizes machine learning to learn an optimization algorithm automatically from data, has gained arising attention in recent years. A generic L2O approach parameterizes the iterative update rule and learns the update direction as a black-box network. While the generic approach is widely applicable, the learned model can overfit and may not generalize well to out-of-distribution test sets. In this paper, we derive the basic mathematical conditions that successful update rules commonly satisfy. Consequently, we propose a novel L2O model with a mathematics-inspired structure that is broadly applicable and generalized well to out-of-distribution problems. Numerical simulations validate our theoretical findings and demonstrate the superior empirical performance of the proposed L2O model.

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