Efficient Robust Global Optimization for Simulation-based Problems using Decomposed Gaussian Processes: Application to MPC Calibration

The closed-loop performance of complex systems controlled by advanced optimization-based control algorithms, such as model predictive control (MPC), critically depends on the selection of several tuning parameters that affect the desired cost function in an unknown manner. Due to inherent limitations of trial-and-error tuning methods, there has been an increasing interest in automatic calibration using derivative-free optimization methods such as Bayesian optimization (BO). BO is particularly attractive due to its ability to accommodate noisy and expensive-to-evaluate cost functions; however, standard BO cannot identify solutions that are robust to uncertainty. In this paper, we address this limitation by proposing a new robust auto-tuning algorithm, DRACO, that relies on a decomposed Gaussian process surrogate model of the objective function. We theoretically establish a bound on the number of samples required for DRACO to find a near-optimal robust solution and provide a proof of convergence. We compare DRACO to existing robust black-box optimization algorithms on a benchmark MPC tuning problem, and we show that DRACO consistently outperforms these alternatives under various conditions.