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Convergence : gradient descent 1-param model

How would you prove the convergence of the sequence only for gama in (0;2)?

Captură de ecran 2020-12-28 190121.jpg

I tried using the \(w^{t+1}/w^{t}\) ratio (it should be in (-1, 1) I guess), but I have one extra term \(\gamma*\bar{y}/w^{t}\) ..

Thanks!

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