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* [python-package] add a note about DART in early_stopping docstring

* add note in R docs too

Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

Co-authored-by: José Morales <jmoralz92@gmail.com>

[python-package] allow use of early_stopping_round<=0 to turn off early stopping (fixes #6401) (#6406)

* ignore training set on early stopping callback

* fixes

* lint

* Apply suggestions from code review
Co-authored-by: James Lamb <jaylamb20@gmail.com>

* trigger ci
Co-authored-by: James Lamb <jaylamb20@gmail.com>

* [python-package] add type hints on Booster eval methods

* remove unnecessary changes

* fix hints

* make `log_evaluation` callback pickleable

* make callback tests stricter

* make `record_evaluation` callback picklable

* make `log_evaluation` callback pickleable

* make callback tests stricter

* Turn `early_stopping` into a Callable class

* Fix

* Lint

* Remove print

* Fix order

* Revert "Lint"

This reverts commit 7ca8b557572446888cf793c0082d9a7efd1e29a7.

* Apply suggestion from code review

* Nit

* Lint

* Move callable class outside the func for pickling

* Move _pickle and _unpickle to tests utils

* Add early stopping callback picklability test

* Nit

* Fix

* Lint

* Improve type hint

* Lint

* Lint

* Add cloudpickle to test_windows

* Update tests/python_package_test/test_engine.py

* Fix

* Apply suggestions from code review

* make record_evaluation compatible with cv

* test multiple metrics in cv

* lint

* fix cv with train metric. save stdv as well

* always add dataset prefix to cv_agg

* remove unused function

* Update test_sklearn.py

* Update python_package.yml

* Update python_package.yml

* Update callback.py

* Update callback.py

* [python-package] fix mypy errors in engine.py

* Apply suggestions from code review
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* allow for stdv

* whitespace
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* Update __init__.py

* Update callback.py

* initial changes

* initial version

* better handling of cases

* warn only with positive threshold

* remove early_stopping_threshold from high-level functions

* remove remaining early_stopping_threshold

* update test to use callback

* better handling of cases

* rename threshold to min_delta

enhance parameter description

update tests

* Apply suggestions from code review
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* reduce num_boost_round in tests

* Apply suggestions from code review
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* trigger ci
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>
Co-authored-by: Nikita Titov <nekit94-12@hotmail.com>

* Update __init__.py

* Update Python-API.rst

* Update engine.py

* Update test_utilities.py

* Update sklearn.py

* Update callback.py

* Update callback.py

* Update callback.py

* deprecate advanced args of `train()` and `cv()`

* update Dask test

* improve deducing

* address review comments

* Update callback.py

* Update engine.py

* Update test_sklearn.py

* Update test_basic.py

* Update dask.py

* Update basic.py

* Update basic.py

* Update basic.py

* Update basic.py

* Update callback.py