提出新方法让神经网络求解约束优化时既高效又保证解的可行性。
HoP: Homeomorphic Polar Learning for Hard Constrained Optimization
- 用同胚极坐标映射嵌入网络，确保输出始终满足约束。
- 在各类合成任务和通信应用中，解距最优更近且完全可行。
- 无需惩罚项或修正步骤，可端到端训练，适合工业级优化场景。
约束优化需要高效的求解器，推动了学习型优化（L2O）方法的发展。作为数据驱动方法，L2O利用神经网络快速生成近似解。然而，如何确保神经网络输出同时具备最优性和可行性仍是重大挑战。为此，本文提出同胚极坐标学习（HoP），通过在神经网络中嵌入同胚映射，解决星凸型硬约束优化问题。其双射结构支持端到端训练，无需额外惩罚或修正。性能评估涵盖多种合成优化任务及无线通信中的真实应用场景。结果表明，所有情况下，HoP生成的解均比现有L2O方法更接近最优，且严格保持可行性。
原文摘要 · Abstract (English)
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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