HoP: Homeomorphic Polar Learning for Hard Constrained Optimization
This work addresses the problem of efficient and reliable constrained optimization for fields like wireless communications, representing an incremental improvement by enhancing feasibility in existing L2O approaches.
The paper tackles the challenge of ensuring both optimality and feasibility in learn-to-optimize (L2O) methods for constrained optimization by introducing Homeomorphic Polar Learning (HoP), which embeds homeomorphic mapping in neural networks to solve star-convex hard-constrained problems, achieving solutions closer to the optimum than existing L2O methods while strictly maintaining feasibility across synthetic tasks and real-world wireless communications applications.
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.