Neural network speeds up solving big control optimization problems
Neural Compression of Long ADMM Trajectory for Multiparametric Quadratic Program
Machine Learning
Summary
Solving big optimization problems used in controlling machines and robots can take a long time. The paper introduces a way to teach a neural network to remember the steps of a common algorithm, making it possible to find answers much faster. This approach doesn’t need extra labeled examples because it uses math conditions directly during training. The result is a method that quickly predicts good solutions and improves them with a few fast extra steps, saving time in real applications.
What this means in practice
- •For control engineers: Speed up real-time model predictive control by reducing computation time with neural warm start and few optimization iterations.
- •For robotics developers: Enable faster online optimization in adaptive robot control systems by compressing lengthy iterative solver trajectories into efficient neural network predictions.
Authors
Liang Wu, Honghui Zheng, Bo Yang, Xu Yang, Yilin Mo, Ján Drgoňa
Abstract
Solving large-scale multiparametric quadratic programs (mpQPs) in real time often requires thousands of iterative optimization updates, creating a major computational bottleneck in model predictive control and learning-enabled systems. This paper proposes TQPNet, a self-supervised neural compression framework that learns to compress long ADMM optimization trajectories into a compact neural warm start followed by a few refinement iterations. We derive a low-dimensional ADMM scheme operating on the primal-dual variables $(x,β)$ and show that its iteration admits an equivalent ReLU-layer representation, termed ADMM(ReLU). Building on this insight, TQPNet combines a multilayer perceptron with ReLU activations (MLP(ReLU)) and a small number of unrolled ADMM(ReLU) refinement layers. The network is trained offline using an optimality-condition-informed residual loss, eliminating the need for solver-generated labels. The proposed residual-based framework enables both self-supervised training and online solution certification through adaptive ADMM(ReLU) refinement. Experiments on large-scale mpQPs and real-time MPC applications demonstrate that TQPNet achieves high accuracy, strong generalization, and substantially faster inference than conventional optimization-based methods.