Warm-starting active-set solvers using graph neural networks

2025-11-17

AI Summary

To address the high computational overhead of quadratic programming (QP) solvers in real-time control—where strict timing constraints are critical—this paper proposes a graph neural network (GNN)-based active-set prediction method for efficient warm-starting of dual active-set QP solvers (DAQP). The approach models each QP instance as a structure-aware bipartite graph, enabling the GNN to encode constraint topology and generalize across problem scales. An active-set classifier is trained via supervised learning to predict the initial active set, which is then integrated with DAQP to refine the initialization. Experiments demonstrate that the method substantially reduces the number of solver iterations, achieves significantly faster convergence than cold-start baselines, matches or exceeds the performance of MLP-based predictors, and exhibits strong out-of-distribution generalization to unseen problem dimensions.

Technology Category

• Machine Learning: Active Learning
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Quadratic programming (QP) solvers are widely used in real-time control and optimization, but their computational cost often limits applicability in time-critical settings. We propose a learning-to-optimize approach using graph neural networks (GNNs) to predict active sets in the dual active-set solver DAQP. The method exploits the structural properties of QPs by representing them as bipartite graphs and learning to identify the optimal active set for efficiently warm-starting the solver. Across varying problem sizes, the GNN consistently reduces the number of solver iterations compared to cold-starting, while performance is comparable to a multilayer perceptron (MLP) baseline. Furthermore, a GNN trained on varying problem sizes generalizes effectively to unseen dimensions, demonstrating flexibility and scalability. These results highlight the potential of structure-aware learning to accelerate optimization in real-time applications such as model predictive control.

Problem

• Accelerating quadratic programming solvers for real-time control
• Predicting optimal active sets using graph neural networks
• Reducing computational costs in time-critical optimization applications

Innovation

• Uses graph neural networks to predict active sets
• Represents quadratic programs as bipartite graphs
• Warm-starts solvers to reduce iteration counts