Solving Quadratic Programs via Deep Unrolled Douglas-Rachford Splitting

TL;DR

This paper introduces a neural network-based approach that unrolls a modified Douglas-Rachford splitting algorithm to solve convex quadratic programs more efficiently, reducing iteration counts and solve time while maintaining convergence guarantees.

Contribution

It presents a novel unrolled DR splitting method with a gradient-based update, improving computational efficiency for convex QPs with theoretical convergence assurances.

Findings

Achieves up to 50% reduction in iteration counts

Reduces solve time by 40% on benchmark datasets

Demonstrates scalability across different problem sizes

Abstract

Convex quadratic programs (QPs) are fundamental to numerous applications, including finance, engineering, and energy systems. Among the various methods for solving them, the Douglas-Rachford (DR) splitting algorithm is notable for its robust convergence properties. Concurrently, the emerging field of Learning-to-Optimize offers promising avenues for enhancing algorithmic performance, with algorithm unrolling receiving considerable attention due to its computational efficiency and interpretability. In this work, we propose an approach that unrolls a modified DR splitting algorithm to efficiently learn solutions for convex QPs. Specifically, we introduce a tailored DR splitting algorithm that replaces the computationally expensive linear system-solving step with a simplified gradient-based update, while retaining convergence guarantees. Consequently, we unroll the resulting DR splitting method and present a well-crafted neural network architecture to predict QP solutions. Our method achieves up to 50% reductions in iteration counts and 40% in solve time across benchmarks on both synthetic and real-world QP datasets, demonstrating its scalability and superior performance in enhancing computational efficiency across varying sizes.