Delaunay-based derivative-free optimization via global surrogates with safe and exact function evaluations
Authors: Muhan Zhao, Shahrouz Ryan Alimo, Pooriya Beyhaghi, Thomas R. Bewley
Published in: 2019 IEEE 58th Conference on Decision and Control (CDC) (2019)
Abstract:
Automatic parameter tuning is an important task in real-world (experimental) optimization, in order to safely (e.g. without crashing) explore an unknown environment. Example includes smooth open-loop control of trajectory planning where collisions must be avoided. Delaunay-based derivative-free optimization via Global Surrogate (Δ-DOGS) algorithms are a family of response surface method that efficiently and globally minimizes black-box, computationally expensive, nonconvex optimization problems; however, the challenge of restricting all function evaluations to be "safe" during the parameter tuning process has not yet been addressed in this family of algorithms. In this work, we develop a new, safety-constrained variant of this approach, dubbed S-DOGS, to automatically learn the safe region of parameter space, while simultaneously characterizing and optimizing the utility function under consideration, under the assumption that the underlying safety constraints are Lipschitz continuous and the safe region is connected and compact. Theoretical analysis and experimental results are provided to demonstrate that the resulting method is both efficient in terms of the rate of convergence with the number of function evaluations performed, and guaranteed to converge to the global minimum while respecting the safety constraints.