Unrolled Graph Neural Networks for Constrained Optimization

2025-09-21

AI Summary

This paper addresses constrained optimization by proposing a graph neural network (GNN)-based framework for dual ascent. The method models primal and dual variables as two coupled GNNs, with inter-layer interactions explicitly encoding the primal descent and dual ascent dynamics of the Lagrangian function; an alternating training scheme stabilizes saddle-point search. Key contributions include: (i) the first systematic unrolling of the dual ascent iteration into a learnable GNN architecture; (ii) a constraint-driven loss function that jointly penalizes objective suboptimality and constraint violation; and (iii) an out-of-distribution (OOD)-aware training strategy to enhance generalization. Experiments demonstrate rapid convergence to near-optimal, near-feasible solutions on in-distribution tasks, and significantly superior performance over traditional solvers and existing learning-based methods on OOD constrained optimization problems—highlighting strong generalization across constraint geometries and problem scales.

Technology Category

Constraint Satisfaction and Optimization: Constraint Learning and AcquisitionSearch and Optimization: Learning to SearchMachine Learning: Optimization

Application Category

Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In this paper, we unroll the dynamics of the dual ascent (DA) algorithm in two coupled graph neural networks (GNNs) to solve constrained optimization problems. The two networks interact with each other at the layer level to find a saddle point of the Lagrangian. The primal GNN finds a stationary point for a given dual multiplier, while the dual network iteratively refines its estimates to reach an optimal solution. We force the primal and dual networks to mirror the dynamics of the DA algorithm by imposing descent and ascent constraints. We propose a joint training scheme that alternates between updating the primal and dual networks. Our numerical experiments demonstrate that our approach yields near-optimal near-feasible solutions and generalizes well to out-of-distribution (OOD) problems.

Problem

• Solving constrained optimization problems using unrolled dual ascent algorithm
• Finding saddle points of Lagrangian with coupled graph neural networks
• Achieving near-optimal solutions that generalize to out-of-distribution problems

Innovation

• Unrolled dual ascent algorithm into coupled GNNs
• Primal and dual networks interact at layer level
• Joint training scheme alternates between network updates