where f i (x) are the true objective functions for i = 1, . . . , n, x are a set of control variables and ε i is additive noise which is often assumed to be Gaussian ε i ∼ N (0, σ 2 i ) . When σ i is a constant, the noise is called homoscedastic and when σ i (x) varies at different x the noise is called heteroscedastic.