HoP: Homeomorphic Polar Learning for Hard Constrained Optimization

• URL: http://arxiv.org/abs/2502.00304v1
• Date: Sat, 01 Feb 2025 03:59:15 GMT
• Title: HoP: Homeomorphic Polar Learning for Hard Constrained Optimization
• Authors: Ke Deng, Hanwen Zhang, Jin Lu, Haijian Sun,
• Abstract summary: Constrained optimization demands highly efficient synthetic training approaches. As a data-driven learning method, L2O leverages neural networks efficiently produce approximate solutions. HoP achieves solutions closer to the optimum than existing L2O methods. In all cases, HoP achieves solutions closer to the optimum than existing L2O methods.
• Score: 3.8166443770130822
• License:
• Abstract: Constrained optimization demands highly efficient solvers which promotes the development of learn-to-optimize (L2O) approaches. As a data-driven method, L2O leverages neural networks to efficiently produce approximate solutions. However, a significant challenge remains in ensuring both optimality and feasibility of neural networks' output. To tackle this issue, we introduce Homeomorphic Polar Learning (HoP) to solve the star-convex hard-constrained optimization by embedding homeomorphic mapping in neural networks. The bijective structure enables end-to-end training without extra penalty or correction. For performance evaluation, we evaluate HoP's performance across a variety of synthetic optimization tasks and real-world applications in wireless communications. In all cases, HoP achieves solutions closer to the optimum than existing L2O methods while strictly maintaining feasibility.

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