3 Stochastic zero-order optimization In the question here you want to understand zero order optimization, when you only have access to the function value f(x) instead of the gradient (thinking about Reinforcement Learning)

3 Stochastic zero-order optimization In the question here you want to understand zero order optimization, when you only have access to the function value f(x) instead of the gradient (thinking about Reinforcement Learning). 3 Consider the case when f :Rd + R being a L-smooth function. Now, we implement the following update: for t = 1,2, ...,T, sample &t ~ N(0, o 1) (for 04 > 0), and update: Yt = It + $t (1) It+1 = argmin{f(x)} (2) ze{yt,&t} Show that: For every ot< || \f(x1)||2, we have: E[f((t+1)] = f(xt) – 1 (0:|| f (x+)||2)