Global Optimization of Stochastic Black-Box Functions with Arbitrary Noise Distributions using Wilson Score Kernel Density Estimation
This work addresses the challenge of efficient optimization in robotics for time-expensive, stochastic functions, offering a method that does not require many evaluations or disturbance modeling, though it is incremental as it builds on existing Bayesian optimization frameworks.
The paper tackled the problem of optimizing stochastic black-box functions with arbitrary noise distributions by introducing the Wilson Score Kernel Density Estimator (WS-KDE) to provide reliable confidence bounds, enabling stable global optimization on a wider range of cost functions, as demonstrated in simulations and applied to automated trap design for vibrational part feeders.
Many optimization problems in robotics involve the optimization of time-expensive black-box functions, such as those involving complex simulations or evaluation of real-world experiments. Furthermore, these functions are often stochastic as repeated experiments are subject to unmeasurable disturbances. Bayesian optimization can be used to optimize such methods in an efficient manner by deploying a probabilistic function estimator to estimate with a given confidence so that regions of the search space can be pruned away. Consequently, the success of the Bayesian optimization depends on the function estimator's ability to provide informative confidence bounds. Existing function estimators require many function evaluations to infer the underlying confidence or depend on modeling of the disturbances. In this paper, it is shown that the confidence bounds provided by the Wilson Score Kernel Density Estimator (WS-KDE) are applicable as excellent bounds to any stochastic function with an output confined to the closed interval [0;1] regardless of the distribution of the output. This finding opens up the use of WS-KDE for stable global optimization on a wider range of cost functions. The properties of WS-KDE in the context of Bayesian optimization are demonstrated in simulation and applied to the problem of automated trap design for vibrational part feeders.