ReLU-QP: A GPU-Accelerated Quadratic Programming Solver for Model-Predictive Control

TL;DR

ReLU-QP is a novel GPU-accelerated quadratic programming solver reformulated as a neural network, enabling real-time control in model-predictive control applications with significant speed advantages over CPU solvers.

Contribution

The paper introduces ReLU-QP, a new approach that reformulates ADMM for QPs as a neural network, allowing efficient GPU deployment for high-dimensional control problems.

Findings

ReLU-QP achieves real-time performance on high-dimensional control tasks.

It outperforms CPU-based solvers by an order of magnitude on large-scale problems.

ReLU-QP is competitive with state-of-the-art solvers on small-to-medium problems.

Abstract

We present ReLU-QP, a GPU-accelerated solver for quadratic programs (QPs) that is capable of solving high-dimensional control problems at real-time rates. ReLU-QP is derived by exactly reformulating the Alternating Direction Method of Multipliers (ADMM) algorithm for solving QPs as a deep, weight-tied neural network with rectified linear unit (ReLU) activations. This reformulation enables the deployment of ReLU-QP on GPUs using standard machine-learning toolboxes. We evaluate the performance of ReLU-QP across three model-predictive control (MPC) benchmarks: stabilizing random linear dynamical systems with control limits, balancing an Atlas humanoid robot on a single foot, and tracking whole-body reference trajectories on a quadruped equipped with a six-degree-of-freedom arm. These benchmarks indicate that ReLU-QP is competitive with state-of-the-art CPU-based solvers for small-to-medium-scale problems and offers order-of-magnitude speed improvements for larger-scale problems.