$[10$ points$]$ We have mainly focused on squared loss, but there are other interesting losses in machine learning. Consider the following loss function which we denote by $(z)=$max$(0,-z).$ Let $S$ be a training set $(x^1,y^1),$dots,$(x^m,y^m)$ where each $x^{i}in{R}^n$ and $y^{i}in\{-1,1\}.$ Consider running stochastic gradient descent $($SGD$)$ to find a weight vector $w$ that minimizes $\frac{1}{m}{\displaystyle \underset{i=1}{\overset{m}{}}}(y^i*w^T{x}^i).$ Explain the explicit relationship between this algorithm and the Perceptron algorithm. Recall that for SGD$,$ the update rule when the $i^{th}$ example is picked at random is

$w_{\text{n}\text{e}\text{w}}=w_{\text{o}\text{l}\text{d}}-grad(y^i{w}^T{x}^i)$

Note: You do not need to be overly concerned about the discontinuity at $(0),$ so you can ignore this when calculating the gradient for this problem.