Recent work has shown that machine-learned predictions can provably improve the performance of classic algorithms. In this work, we propose the first minimum-cost network flow algorithm augmented with a dual prediction. Our method is based on a classic minimum-cost flow algorithm, namely $\varepsilon$-relaxation. We provide time complexity bounds in terms of the infinity norm prediction error, which is both consistent and robust. We also prove sample complexity bounds for PAC-learning the prediction. We empirically validate our theoretical results on two applications of minimum-cost flow, i.e., traffic networks and chip escape routing, in which we learn a fixed prediction, and a feature-based neural network model to infer the prediction, respectively. Experimental results illustrate $12.74\times$ and $1.64\times$ average speedup on two applications.

翻译：近期研究表明，机器学习预测可被证明提升经典算法的性能。本文提出了首个结合对偶预测的最小代价网络流算法。该方法基于经典的最小代价流算法——$\varepsilon$-松弛算法。我们基于无穷范数预测误差给出了时间复杂度界，该界兼具一致性与鲁棒性。同时证明了PAC学习预测的样本复杂度界。我们在最小代价流的两个应用场景（交通网络与芯片逃逸布线）中实证验证了理论结果：分别采用固定预测学习和基于特征的神经网络模型推断预测。实验结果表明，在两个应用场景中分别实现了平均$12.74\times$和$1.64\times$的加速比。