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.

翻译：我们提出ReLU-QP，一种GPU加速的二次规划（QP）求解器，能够以实时速率求解高维控制问题。ReLU-QP通过将用于求解QP的交替方向乘子法（ADMM）算法精确重新表述为一个具有修正线性单元（ReLU）激活函数的深层权值共享神经网络而推导得出。这种重新表述使得能够利用标准机器学习工具包将ReLU-QP部署于GPU上。我们通过三个模型预测控制（MPC）基准测试评估了ReLU-QP的性能：在控制约束下稳定随机线性动力系统、使Atlas仿人机器人单足平衡，以及跟踪配备六自由度机械臂的四足机器人的全身参考轨迹。这些基准测试表明，对于中小规模问题，ReLU-QP与最先进的基于CPU的求解器具有竞争力，而对于大规模问题，则能提供数量级的速度提升。