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arXiv · 2305.18577

Towards Constituting Mathematical Structures for Learning to Optimize

Jialin Liu·Xiaohan Chen·Zhangyang Wang·Wotao Yin·HanQin Cai
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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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Jialin Liu, Xiaohan Chen, Zhangyang Wang, Wotao Yin, HanQin Cai. 2023-05-29. Towards Constituting Mathematical Structures for Learning to Optimize. https://arxiv.org/abs/2305.18577

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