As a result of #15123, we now have a common private loss function module under sklearn._loss. In sklearn.linear_models we have 2 algorithms that need Cython version that calculate losses and gradients on single values (not on arrays), namely

• _plain_sgd as used in SGDClassifier, SGDRegressor and SGDOneClassSVM; and
• sag_solver as used in LogisticRegression.

My plan is to break this migration into smaller steps:

1. DEP deprecate loss_function_ attribute in SGDClassifier and SGDOneClassSVM #27979 Deprecate loss_function_ attribute in v1.4 which gives access to the Cython loss functions that we want to replace.
2. MNT replace Cython loss functions in SGD part 1 #27999 change order of Cython loss function arguments to align with the ones in sklearn._loss.
3. Carry out the deprecation after release 1.5 (to be released with 1.6)
   MNT remove deprecated loss_function_ in SGD #29095
4. ENH replace Cython loss functions in SGD part 2 #28029 Replace Cython losses with the ones from sklearn._loss, except multinomial one
5. MNT replace Cython loss functions in SGD part 3 #28037 Replace the multinomial loss