Add automatic best model loading to Trainer (#7431)

* Add automatic best model loading to Trainer

* Some small fixes

* Formatting

src/transformers/training_args.py

@@ -145,6 +145,28 @@ class TrainingArguments:
             Will eventually default to :obj:`["labels"]` except if the model used is one of the
             :obj:`XxxForQuestionAnswering` in which case it will default to
             :obj:`["start_positions", "end_positions"]`.
+        load_best_model_at_end (:obj:`bool`, `optional`, defaults to :obj:`False`):
+            Whether or not to load the best model found during training at the end of training.
+
+            .. note::
+
+                When set to :obj:`True`, the parameters :obj:`save_steps` will be ignored and the model will be saved
+                after each evaluation.
+        metric_for_best_model (:obj:`str`, `optional`)
+            Use in conjunction with :obj:`load_best_model_at_end` to specify the metric to use to compare two different
+            models. Must be the name of a metric returned by the evaluation with or without the prefix :obj:`"eval_"`.
+            Will default to :obj:`"loss"` if unspecified and :obj:`load_best_model_at_end=True` (to use the evaluation
+            loss).
+
+            If you set this value, :obj:`greater_is_better` will defaut to :obj:`True`. Don't forget to set it to
+            :obj:`False` if your metric is better when lower.
+        greater_is_better (:obj:`bool`, `optional`)
+            Use in conjunction with :obj:`load_best_model_at_end` and :obj:`metric_for_best_model` to specify if better
+            models should have a greater metric or not. Will default to:
+
+            - :obj:`True` if :obj:`metric_for_best_model` is set to a value that isn't :obj:`"loss"` or
+              :obj:`"eval_loss"`.
+            - :obj:`False` if :obj:`metric_for_best_model` is not set, or set to :obj:`"loss"` or :obj:`"eval_loss"`.
     """
 
     output_dir: str = field(
@@ -287,6 +309,17 @@ class TrainingArguments:
         default=None, metadata={"help": "The list of keys in your dictionary of inputs that correspond to the labels."}
     )
 
+    load_best_model_at_end: Optional[bool] = field(
+        default=False,
+        metadata={"help": "Whether or not to load the best model found during training at the end of training."},
+    )
+    metric_for_best_model: Optional[str] = field(
+        default=None, metadata={"help": "The metric to use to compare two different models."}
+    )
+    greater_is_better: Optional[bool] = field(
+        default=None, metadata={"help": "Whether the `metric_for_best_model` should be maximized or not."}
+    )
+
     def __post_init__(self):
         if self.disable_tqdm is None:
             self.disable_tqdm = logger.getEffectiveLevel() > logging.WARN
@@ -304,6 +337,11 @@ class TrainingArguments:
         if self.eval_steps is None:
             self.eval_steps = self.logging_steps
 
+        if self.load_best_model_at_end and self.metric_for_best_model is None:
+            self.metric_for_best_model = "loss"
+        if self.greater_is_better is None and self.metric_for_best_model is not None:
+            self.greater_is_better = self.metric_for_best_model not in ["loss", "eval_loss"]
+
     @property
     def train_batch_size(self) -> int:
         """