I am trying to learn multiple linear regression using MATLAB. I am using Weight (x1) and Horsepower (x2) as features to predict the mileage (y) of the vehicle.
So, the model would be $y_{est}= w_1x_1+w_2x_2+b$.
I am using gradient descent to find the point of minimum corresponding to $J(w_1,w_2,b)=$ mean$[(y-y_{est})^{2}]$.
My question is when I use step size $\alpha$ to move along the negative direction of gradients w.r.t each of $w_1, w_2$ and $b$, do I need to use a different step size for each of these three parameters?
Usually, in the notes that I am following, they use a single $\alpha$ for all the three parameters.
Can someone explain why this is sufficient? Because, I would ideally think that having same alpha can cause issues for convergence.