2. We are trying to predict whether a certain chemical reaction will take place as a function of our experimental conditions: temperature, pressure, concentration of catalyst, and several other factors. For each experiment i = 1, ...,m we record the experimental conditions in the vector a; ( R" and the outcome in the scalar b; 6 {-1, 1} (+1 if the reaction occurred and -1 if it did not). We will train our linear classifier to minimize hinge loss. Namely, we solve: minimize E(1 - b,x] w)+ where (u)+ = max(0, u) is the hinge loss operator i=1 a) Derive a gradient descent method for solving this problem. Explicitly give the computations required at each step. Note: you may ignore points where the function is non-differentiable. b) Explain what happens to the algorithm if you land at a w* that classifies all the points perfectly, and by a substantial margin