In the question here you want to understand zero order optimization, when you only have access...

   

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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). Consider the case when f: RR being a L-smooth function. Now, we implement the following update: for t=1,2,... ,T, sample &~ N(0,021) (for o, > 0), and update: N Show that: For every ot Y₁ = x₁ + & 2+1 = argmin{f(2)} Vf(x)|2 we have: 2L√d Ef(-1)] ≤ f(x)-(o|Vf(xi)||2₂) (1) (2) 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). Consider the case when f: RR being a L-smooth function. Now, we implement the following update: for t=1,2,... ,T, sample &~ N(0,021) (for o, > 0), and update: N Show that: For every ot Y₁ = x₁ + & 2+1 = argmin{f(2)} Vf(x)|2 we have: 2L√d Ef(-1)] ≤ f(x)-(o|Vf(xi)||2₂) (1) (2)

Answer rating: 100% (QA)

Solution We can prove the statement by using induction First we will assume that ot Vfx2 2Ld ... View the full answer