Zero-Order Optimization for Gaussian Process-based Model Predictive Control

By enabling constraint-aware online model adaptation, predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention the learning-based community. Yet, solving resulting optimal problem real-time generally remains a major challenge, due to i) increased number of augmented states optimization problem, as well ii) computationally expensive evaluations posterior mean covariance their respective derivatives. To tackle these challenges, we employ tailored Jacobian approximation sequential quadratic programming (SQP) approach combine it with parallelizable GP inference automatic differentiation framework. Reducing numerical complexity respect state dimension nx for each SQP iteration from O(nx6) O(nx3), accelerating on graphical processing unit, proposed algorithm computes suboptimal, yet feasible, solutions at drastically reduced computation times exhibits favorable local convergence properties. Numerical experiments verify scaling properties investigate runtime distribution across different parts algorithm.