  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.
