Given a separable data (x_1,y_1 ),...,(x_m,y_m ),x_i in R^d,y_i in {+1,-1},i in [m], show that the modified Perceptron (w^((t+1))=w^((t))+\\\\eta y_i x_i ) is exactly same as optimizing the following loss function using stochastic gradient descent (where we choose a single point to evaluate the gradient of the loss function) with learning rate \\\\eta . The loss function is given by:\ _(i in M)-y_i (w^ x_i )\ where M indexes the set of misclassified points. This loss function is non negative and proportional to the distance of the misclassified points to the decision boundary w^ x=0.