Stochastic gradient Descent implementation - MATLAB

Question

I'm trying to implement "Stochastic gradient descent" in MATLAB. I followed the algorithm exactly but I'm getting a VERY VERY large w (coffients) for the prediction/fitting function. Do I have a mistake in the algorithm ?

The Algorithm :

x = 0:0.1:2*pi      // X-axis
    n = size(x,2);      
    r = -0.2+(0.4).*rand(n,1);  //generating random noise to be added to the sin(x) function

    t=zeros(1,n);
    y=zeros(1,n);



    for i=1:n
        t(i)=sin(x(i))+r(i);          // adding the noise
        y(i)=sin(x(i));               // the function without noise
    end

    f = round(1+rand(20,1)*n);        //generating random indexes

    h = x(f);                         //choosing random x points
    k = t(f);                         //chossing random y points

    m=size(h,2);                     // length of the h vector

    scatter(h,k,'Red');              // drawing the training points (with noise)
    %scatter(x,t,2);
    hold on;
    plot(x,sin(x));                 // plotting the Sin function


    w = [0.3 1 0.5];                    // starting point of w
    a=0.05;                         // learning rate "alpha"

// ---------------- ALGORITHM ---------------------//
    for i=1:20
        v = [1 h(i) h(i).^2];                      // X vector
        e = ((w*v') - k(i)).*v;            // prediction - observation
        w = w - a*e;                       // updating w
    end

    hold on;

    l = 0:1:6;
    g = w(1)+w(2)*l+w(3)*(l.^2);
    plot(l,g,'Yellow');                      // drawing the prediction function

Answer 1

If you use too big learning rate, SGD is likely to diverge.
The learing rate should converge to zero.

Answer 2

typically, if w ended up with too large values, there is overfitting. I didn't really look at your code carefully. But I think, what is missing from your code is a proper regularization term, which prevents the training overfitting. Also, here:

e = ((w*v') - k(i)).*v;

The v here is not the gradient of the predicted value, isn't it? According to algorithm, you should replace it. Let's see how it will be like after doing this.