Currently the optimization routine returns the x_i with smallest y_i observed. While this makes sense with deterministic functions, it doesn't make that much sense with stochastic functions where the minimum of the mean doesn't always coincide with the sample minimum. For this reason, it would be good to have an option for retrieving the minimum of the mean function instead of the minimum sampled value.
Currently the optimization routine returns the x_i with smallest y_i observed. While this makes sense with deterministic functions, it doesn't make that much sense with stochastic functions where the minimum of the mean doesn't always coincide with the sample minimum. For this reason, it would be good to have an option for retrieving the minimum of the mean function instead of the minimum sampled value.