用图神经网络预测优化约束，加速实时控制中的求解过程。
Warm-starting active-set solvers using graph neural networks
- 将二次规划问题建模为二分图，用GNN预测最优活动约束集。
- 相比冷启动，迭代次数显著减少，且在不同规模问题上表现稳定。
- 能泛化到未见问题规模，适合模型预测控制等实时场景。
二次规划（QP）求解器广泛应用于实时控制与优化，但计算成本常限制其在时间敏感场景中的使用。为此，我们提出一种基于图神经网络（GNN）的学习优化方法，用于预测双权重主动集求解器DAQP中的活动约束。该方法通过将QP问题表示为二分图，利用结构特性学习近似最优活动集，从而有效实现求解器的热启动。在不同问题规模下，该GNN方法均显著减少求解迭代次数，性能与多层感知机基线相当。相较于基线，本方法在多种问题规模上训练后仍可泛化至未见维度，展现出良好的灵活性与可扩展性。结果表明，结构感知学习在加速实时优化（如模型预测控制）方面具有巨大潜力。
原文摘要 · Abstract (English)
Quadratic programming (QP) solvers are widely used in real-time control and optimization, but their computational cost often limits applicability in time-critical settings. To resolve this, we propose a learning-to-optimize approach using graph neural networks (GNNs) to predict active constraints in the dual active-set solver DAQP. Our method exploits the structural properties of QPs by representing them as bipartite graphs and learns to approximate the optimal active set for effectively 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 baseline. In contrast to the baseline, our GNN-based approach trained on varying problem sizes generalizes 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.
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