Expensive multiobjective optimization for robotics with consideration of heteroscedastic noise

In many robotic problems, optimization of the policy for multiple conflicting criteria is required. However this is very challenging due to the existence of noise, which may be input dependent, or heteroscedastic, and the restriction in the number of evaluations, due to robotic experiments which are expensive in time and/or money. This paper presents a multiobjective optimization (MOO) algorithm for expensive-to-evaluate noisy functions for robotics. We present a method for model selection between heteroscedastic and standard homoscedastic Gaussian process regression techniques to create suitable surrogate functions from noisy samples and find the point to be observed at the next step. This algorithm is compared against an existing MOO algorithm which assumes homoscedastic noise, and is then used to optimize the speed and head stability of the sidewinding gait of a snake robot.