Minimum-Cost Network Flow with Dual Predictions
Zhiyang Chen, Hailong Yao, Xia Yin
TL;DR
This work introduces the first minimum-cost network flow algorithm augmented with dual predictions within the ε-relaxation framework. By warm-starting with a learned dual solution and augmenting with cost scaling, the authors derive theoretical bounds that interpolate between worst-case performance and fast convergence when predictions are accurate, and they prove PAC-learning guarantees for the predictor. They demonstrate significant empirical speedups on traffic networks and escape routing, and provide practical learning strategies for both fixed and feature-based predictors, including a CNN-based dual predictor implemented via a UNet architecture. The results show that combining dual predictions with ε-relaxation yields robust, scalable improvements for large-scale MCFlow instances, with potential applicability to broader linear-programming problems and learning-augmented optimization. Overall, the paper advances learning-augmented optimization by delivering rigorous guarantees and tangible performance gains in a core combinatorial problem.
Abstract
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.