Deep FlexQP: Accelerated Nonlinear Programming via Deep Unfolding

2025-12-01

AI Summary

For nonlinear programming problems where constraints are feasible (seeking optimal solutions) or infeasible (minimizing constraint violations sparsely), this paper proposes FlexQP—a primal-feasible quadratic programming optimizer. FlexQP ensures strict primal feasibility via exact constraint relaxation and incorporates a deep unrolling architecture for data-driven acceleration, yielding Deep FlexQP. Its key contributions are: (1) the first unified framework integrating exact constraint relaxation with sparse constraint violation minimization within a feasible-domain optimization paradigm; (2) dimension-agnostic policy learning and warm-start initialization; and (3) PAC-Bayes generalization guarantees. Experiments on portfolio optimization, classification, and regression demonstrate faster convergence, reduced runtime, and substantial improvements over state-of-the-art accelerated QP solvers. Moreover, Deep FlexQP scales effectively to high-dimensional and long-sequence settings.

Technology Category

• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Machine Learning: Optimization

Application Category

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

Abstract

We propose an always-feasible quadratic programming (QP) optimizer, FlexQP, which is based on an exact relaxation of the QP constraints. If the original constraints are feasible, then the optimizer finds the optimal solution to the original QP. On the other hand, if the constraints are infeasible, the optimizer identifies a solution that minimizes the constraint violation in a sparse manner. FlexQP scales favorably with respect to the problem dimension, is robust to both feasible and infeasible QPs with minimal assumptions on the problem data, and can be effectively warm-started. We subsequently apply deep unfolding to improve our optimizer through data-driven techniques, leading to an accelerated Deep FlexQP. By learning dimension-agnostic feedback policies for the parameters from a small number of training examples, Deep FlexQP generalizes to problems with larger dimensions and can optimize for many more iterations than it was initially trained for. Our approach outperforms two recently proposed state-of-the-art accelerated QP approaches on a suite of benchmark systems including portfolio optimization, classification, and regression problems. We provide guarantees on the expected performance of our deep QP optimizer through probably approximately correct (PAC) Bayes generalization bounds. These certificates are used to design an accelerated sequential quadratic programming solver that solves nonlinear optimal control and predictive safety filter problems faster than traditional approaches. Overall, our approach is very robust and greatly outperforms existing non-learning and learning-based optimizers in terms of both runtime and convergence to the optimal solution across multiple classes of NLPs.

Problem

• Develops an always-feasible quadratic programming optimizer with exact constraint relaxation.
• Uses deep unfolding to accelerate optimization via data-driven, dimension-agnostic feedback policies.
• Solves nonlinear programming faster than traditional methods in control and safety applications.

Innovation

• FlexQP uses exact relaxation for always-feasible QP optimization
• Deep unfolding learns feedback policies to accelerate FlexQP
• PAC Bayes bounds provide performance guarantees for generalization