aiqbench analysis
This paper trains a small ReLU network to predict warm starts for ADMM, a classical optimization solver, and then refines them with a few unrolled iterations. It is trained without solver-generated labels, using an optimality-residual loss, and the residual also serves as a certificate at inference time. For ML readers, the useful part is the self-supervised, residual-certified approach to learned optimization for real-time control. The reported speedups are relative to conventional solvers and would need independent benchmarking on specific MPC workloads.
Neural Compression of Long ADMM Trajectory for Multiparametric Quadratic Program
arXiv:2610.38079v1 Announce Type: cross 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 $(x,\beta)$ 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.
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 $(x,\beta)$ 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.
Accepted at NeurIPS 2026. Code: this https URL
Optimization and Control (math.OC); Machine Learning (cs.LG); Systems and Control (eess.SY)
arXiv:2610.38079 [math.OC]
(or arXiv:2610.38079v1 [math.OC] for this version)
https://doi.org/10.48550/arXiv.2610.38079 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 267 words