Classifying points exactly on decision boundary
It is up to the user how they want to handle such cases. The loss for the points on the decision boundary will be 0. It's a design decision the user has to take. One example could be to consider such cases in misclassification and update your weights while training. 

If $y (w \cdot x + b) &gt; 0$: $\text{no loss}$

If $y (w \cdot x + b) \leq 0$: $\text{loss} = −y (w \cdot x + b)$ 

During inference, if such cases arise, you can call a random classifier to classify it in one of the classes.