Warm-starting active-set solvers using graph neural networks
This work addresses efficiency in real-time control and optimization, such as model predictive control, but is incremental as it builds on existing learning-to-optimize approaches with structure-aware methods.
The paper tackled the computational cost of quadratic programming (QP) solvers in time-critical settings by using graph neural networks (GNNs) to predict active sets for warm-starting, reducing solver iterations across varying problem sizes with effective generalization to unseen dimensions.
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.