面向大规模线性规划的PDHG展开学习优化方法
PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Linear Programming
AI总结：
本文提出PDHG-Net及两阶段学习优化方法，将PDHG算法展开为神经网络并结合信道扩展技术，先用网络生成近似解再用PDHG算法精化，在大规模线性规划求解中实现最高3倍加速。
摘要：
求解大规模线性规划（LP）问题是通信网络、电力系统、金融和物流等多个领域中的重要任务。近年来，出现了两种不同的加速LP求解的方法：（i）一阶方法（FOMs）；（ii）学习优化（L2O）。在本工作中，我们提出了一种称为PDHG-Net的FOM展开神经网络（NN），并提出了一种两阶段L2O方法来求解大规模LP问题。新架构PDHG-Net通过将最近出现的PDHG方法展开为神经网络而设计，并结合了借鉴自图神经网络的信道扩展技术。我们证明了所提出的PDHG-Net能够恢复PDHG算法，因此可以用多项式数量的神经元逼近LP实例的最优解。我们提出了一种两阶段推理方法：首先使用PDHG-Net生成近似解，然后应用PDHG算法进一步改进该解。实验表明，我们的方法能够显著加速LP求解，在大规模LP问题上与FOMs相比实现了高达3倍的加速。
英文摘要：
Solving large-scale linear programming (LP) problems is an important task in various areas such as communication networks, power systems, finance and logistics. Recently, two distinct approaches have emerged to expedite LP solving: (i) First-order methods (FOMs); (ii) Learning to optimize (L2O). In this work, we propose an FOM-unrolled neural network (NN) called PDHG-Net, and propose a two-stage L2O method to solve large-scale LP problems. The new architecture PDHG-Net is designed by unrolling the recently emerged PDHG method into a neural network, combined with channel-expansion techniques borrowed from graph neural networks. We prove that the proposed PDHG-Net can recover PDHG algorithm, thus can approximate optimal solutions of LP instances with a polynomial number of neurons. We propose a two-stage inference approach: first use PDHG-Net to generate an approximate solution, and then apply PDHG algorithm to further improve the solution. Experiments show that our approach can significantly accelerate LP solving, achieving up to a 3$\times$ speedup compared to FOMs for large-scale LP problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
