DOC: optimize.least_squares: better name for default `loss`?

Hi everybody, And thank you all for the great job. I’ve a question about how curve_fit() solves least squares problems when boundaries are provided.
Specifically, reading the docs here (https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html) it is explicitly said: “Use non-linear least squares to fit a function, f, to data.” However, and please correct me if I’m wrong, if the problem involves boundaries, the function calls least_squares(), that according to the docs (https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.html#scipy.optimize.least_squares) by default has method='trf' and loss='linear', therefore the problem is addressed as “a standard least-squares problem”. So, if I understood correctly, by default in curve_fit() if we don’t pass an alternative loss function supported by least_squares() we are treating a case of a standard linear least squares. If this is the case, IMHO the docs of curve_fit() would be more precise if rephrased as: “Use linear least squares to fit a function, f, to data. Supports non-linear least squares.”

[mdhaber]

Thanks. If it comes up again, we’ll consider changing something. For now, it says “‘linear’…Gives a standard least-squares problem”, which is clear enough, whatever “linear” is supposed to refer to. So I’ll go ahead and close.

[steppi]

The strings that are accepted by loss were selected to correspond with the overall “loss function”; they are not descriptions of rho. Therefore, even though rho(x) = x is an identity operation, 'l2' is a better name for rho(x) = x than 'identity' because it leads to an L2 loss function. And 'l2' is a better name than 'linear' because 'linear' describes neither rho nor the loss function.

Right, every string besides 'linear' refers to the overall cost function, not rho. I think 'l2' would be a better name because it follows the same convention as 'soft_l1', 'huber', etc.

(Would “quadratic” also work?)

Yes, that seems fine to me.

But on the other hand, the function name is least_squares. With that in mind, maybe loss should describe what is done with the squared errors. In that case, 'linear' makes some sense : the loss function is a linear combination of the squares of the errors (with all coefficients 1)?

Yes, in isolation it makes sense. It just doesn’t follow the same convention as the other strings, which all describe the overall cost function. I think that’s a little confusing, although maybe it’s not worth spending the effort to change things.