Non convex optimization

[combat1818]

Hi, I've been struggling with this task and would really appreciate some help:
We are given a function $$f: R^{d}->R$$ it is differentiable, L-smooth and non-convex, it has a global minimum $$x^{*}$$We use a version of gradient descent of the form: $$x_{t+1}=x_{t}- \eta_{t}\frac{\nabla f(x_{t})}{||\nabla f(x_{t})|| + \beta_{t}}$$ where $$\eta_t,\beta_t>0$$We want to find $$\eta_t, \beta_t$$ which do not depend on the parameter L and guarantee:
$$\frac{1}{T} \sum_{t=0}^{T-1} ||\nabla f(x_t)||=\tilde{O}(T^{\frac{-1}{2}})$$where the O tilde notation ignores logarithmic factors.

 

[mmm4444bot]

I've been struggling with this task

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