$11.(10$ points$)$ Consider a supervised learning problem, we define an error for a single data point $($In$,$ Yn$)$ to be en $($w$)=$ max$(0,-$ynw$+$xn$)$ where In is the feature, yn is the label and w is the weight we want to learn in the hypothesis. Argue that Perceptron Learning Algorithm $($PLA$)$ can be viewed as Stochastic Gradient Descent $($SGD$)$ on en with learning rate n $=1.$ Hint: Recall the vector form of PLA as h$($x$)=$ sign$($wx$)$ and the update rule of PLA is w$($t $+1)$ w$($t$)+$ y$($t$)$x$($t$),$ where $($z$($t$),$ y$($t$))$ is misclassified example at iteration t$.$ The weight update in SGD is w w $-$ nVen$($w$)$