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$1),...,($xm$,$ ym$)$ where each xi in Rn and yi in $\{1,1\}.$ Con$-$

sider running stochastic gradient descent $($SGD$)$ to find a weight vector w that minimizes

$1$

m

Pm

i$=1($yi $$ wT xi$).$ Explain the explicit relationship between this algorithm and the Per$-$

ceptron algorithm. Recall that for SGD$,$ the update rule when the ith example is picked at

random is

wnew $=$ wold $\backslash$eta $$ yiwT xi