  Parallel black box optimization consists in estimating the optimum of a
function using $\lambda$ parallel evaluations of $f$. Averaging the $\mu$ best
individuals among the $\lambda$ evaluations is known to provide better
estimates of the optimum of a function than just picking up the best. In
continuous domains, this averaging is typically just based on (possibly
weighted) arithmetic means. Previous theoretical results were based on
quadratic objective functions. In this paper, we extend the results to a wide
class of functions, containing three times continuously differentiable
functions with unique optimum. We prove formal rate of convergences and show
they are indeed better than pure random search asymptotically in $\lambda$. We
validate our theoretical findings with experiments on some standard black box
functions.
