Noisy Optimization Problem u Without noise With noises, Additive min f(x),x=[x1, x2, ,x d x∈X (x)=f(x)+N(0,72) d is the number of dimensions 12. Multiplicative: x is the feasible region of x (x)=(x)XN(12)Noisy Optimization Problem ◼ Without noise: min 𝑥∈𝑋 𝑓(𝑥) , 𝑥 = [𝑥 1 , 𝑥 2 , … , 𝑥 𝑑 ] 𝑑 is the number of dimensions. 𝑋 is the feasible region of 𝑥. ◼ With noises: 1. Additive: 𝑓 መ + 𝑥 = 𝑓 𝑥 + 𝑁 0,𝜎 2 2. Multiplicative: 𝑓 መ × 𝑥 = 𝑓 𝑥 × 𝑁(1,𝜎 2 )