Funneled Bayesian Optimization for Design, Tuning and Control of Autonomous Systems

In this paper, we tackle several problems that appear in robotics and autonomous systems: algorithm tuning, automatic control, and intelligent design. All those problems share in common that they can be mapped to global optimization problems where evaluations are expensive. Bayesian optimization (BO) has become a fundamental global optimization algorithm in many problems where sample efficiency is of paramount importance. BO uses a probabilistic surrogate model to learn the response function and reduce the number of samples required. Gaussian processes (GPs) have become a standard surrogate model for their flexibility to represent a distribution over functions. In a black-box settings, the common assumption is that the underlying function can be modeled with a stationary GP. In this paper, we present a novel kernel function specially designed for BO, that allows nonstationary behavior of the surrogate model in an adaptive local region. This kernel is able to reconstruct nonstationarity even with the irregular sampling distribution that arises from BO. Furthermore, in our experiments, we found that this new kernel results in an improved local search (exploitation), without penalizing the global search (exploration) in many applications. We provide extensive results in well-known optimization benchmarks, machine learning hyperparameter tuning, reinforcement learning, and control problems, and UAV wing optimization. The results show that the new method is able to outperform the state of the art in BO both in stationary and nonstationary problems.