# 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.
• Adding to what @Dave pointed out, when optimizing a perceptron you are essentially compute the loss for each input in your training dataset and sum that. To do that you need to traverse the full training data set, which is exactly what $\sum_{x_i \in M}$ means. Jun 12 '19 at 4:36