发表机构
Oberlin College; University of California, San Diego; OneChronos（欧柏林学院; 加州大学圣迭戈分校; OneChronos）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于PDHG的图消息传递框架GraphPDHG，用于高效求解图鞍点问题，并可作为二阶优化的热启动，提升规模泛化能力。
AI 中文摘要
神经算法推理，即将神经网络与算法范式对齐，已成为解决多项式时间可解和计算上更难的组合优化问题的一种方法。我们提出了一种基于Chambolle-Pock原始-对偶混合梯度（PDHG）方法的新的消息传递框架，称为GraphPDHG，用于求解一般的图鞍点问题。理论上，我们证明GraphPDHG可以通过模拟PDHG高效地求解一类图鞍点问题。我们还表明，我们的网络可以学习加速的PDHG算法。实验上，我们通过评估我们的模型作为二阶优化技术（SSNAL）的学习热启动的性能来支持我们在加速PDHG上的结果。我们还表明，与PDHG的对齐比非对齐的图神经网络（GNN）基线具有更强的规模泛化能力。总体而言，我们提出了一种新颖的架构，用于求解图上的通用优化问题族。
英文摘要
Neural algorithmic reasoning, or aligning a neural network with an algorithmic paradigm, has emerged as an approach to solving polynomial-time-solvable and computationally harder combinatorial optimization problems. We propose a new message-passing framework based on the Chambolle-Pock Primal--Dual Hybrid Gradient (PDHG) method called \textsc{GraphPDHG} for solving general graph saddle-point problems. Theoretically, we show that \textsc{GraphPDHG} can efficiently solve a family of graph saddle-point problems by simulating PDHG. We also show that our network can learn an accelerated PDHG algorithm. Experimentally, we support our results on accelerated PDHG by evaluating the performance of our model as a learned warm start for second-order optimization techniques (SSNAL). We also show that alignment with PDHG leads to stronger size generalization than non-aligned graph neural network (GNN) baselines. Overall, we propose a novel architecture for solving a general family of optimization problems on graphs.
