Metric doc update (#1325)

* update sklearn fit parameter description

* update mtric parameter description

docs/Parameters.rst

@@ -594,7 +594,12 @@ Metric Parameters
 
 -  ``metric``, default=\ ``''``, type=multi-enum
 
-   -  if \ ``''`` (empty string or not specific), metric corresponding to specified application will be used
+   - metric to be evaluated on the evaluation sets **in addition** to what is provided in the training arguments
+
+      -  ``''`` (empty string or not specific), metric corresponding to specified objective will be used
+         (this is possible only for pre-defined objective functions, otherwise no evaluation metric will be added)
+
+      - ``'None'`` (string **not** a ``None`` value), no metric registered, alias=\ ``na``
    
       -  ``l1``, absolute loss, alias=\ ``mean_absolute_error``, ``mae``, ``regression_l1``
    
@@ -638,7 +643,7 @@ Metric Parameters
    
       -  ``kldiv``, `Kullback-Leibler divergence`_, alias=\ ``kullback_leibler``
 
-   -  support multi metrics, separated by ``,``
+   -  support multiple metrics, separated by ``,``
 
 -  ``metric_freq``, default=\ ``1``, type=int, alias=\ ``output_freq``
 

python-package/lightgbm/sklearn.py

@@ -321,8 +321,10 @@ class LGBMModel(_LGBMModelBase):
         eval_metric : string, list of strings, callable or None, optional (default=None)
             If string, it should be a built-in evaluation metric to use.
             If callable, it should be a custom evaluation metric, see note for more details.
+            In either case, the ``metric`` from the model parameters will be evaluated and used as well.
         early_stopping_rounds : int or None, optional (default=None)
             Activates early stopping. The model will train until the validation score stops improving.
+            If there's more than one, will check all of them.
             Validation error needs to decrease at least every ``early_stopping_rounds`` round(s)
             to continue training.
         verbose : bool, optional (default=True)