3.

Consider the perceptron learning algorithm using (batch) gradient descent, discussed in the class. We will assume that the data is defined using two features (x₁ and x₂). We are interested in learning the perceptron boundary by training on the following training data:

x1	x2	y
0.80	0.20	1
0.90	0.25	1
0.30	0.70	-1
0.25	0.65	-1

Initialize the weight vector to all 1s and the run the gradient descent algorithm with learning rate, eta = 0.2. After two updates of the weight vector, which of the following will be true (round the decimals to first two significant digits). Assume that we take care of the intercept term by absorbing the intercept term into the beginning of the weight vector.

		a)	The gradient of the objective function with respect to the augmented weights, just before the second update is [-1.95, 0.14]
		b)	The squared loss value for the updated perceptron after second update on the training data is 2.05
		c)	The weight vector w after two iterations will be [-0.61, 0.31, 0.11]
		d)	The perceptron after second update makes 0 mistakes on the training data