Is it a acceptable way to write a loss function in this form? I found a loss function of a perceptron on a book is in this form 

$$ L(w,b) = - \sum\limits_{x_i \in M}y_i(wx_i+b) $$

In the context of machine learning loss functions, is it acceptable to put $x_i$ on the bottom of a summation notation?
It just means to sum over all $x_i$ in $M$. That is completely acceptable notation.