Machine Learning - SVM - How to calculate bias when calculate vector W?

Question

I am writing code of SVM Primal that uses SGD (Stochastic SubGradient Descent) for optimize the vector W.

The classification methos is sign(w*x + bias).
My question is how to find the best bias for it?
I guess that it has to do during the W optimizing, but how? I have no idea.

Answer 1

Your hypothesis is sign(<w, x> + b), think for a second about x' = [x 1], then you could express your hypothesis as sign(<w', x'>), where w' = [w b]. I hope it clearly shows that b is not any different from w's (the only difference is that your regularizing term ||w||^2 does not involve b). Thus you just need d L/ d b where L is your loss function.