Update doc for metric_for_best_model when save_strategy="best". (#35389)

* Updated docstring for _determine_best_metric.

* Updated docstring for metric_for_best_model.

* Added test case for save strategy.

* Updated incorrect test case.

* Changed eval_strategy to match save_strategy.

* Separated test cases for metric.

* Allow load_best_model when save_strategy == "best".

* Updated docstring for metric_for_best_model.

tests/trainer/test_trainer.py

@@ -4220,7 +4220,9 @@ class TrainerIntegrationTest(TestCasePlus, TrainerIntegrationCommon):
                     total=total,
                 )
 
-        # Case 3: Metric name not provided; throw error.
+    def test_metric_for_best_model_behavior(self):
+        # Case 1: Metric name not provided when `save_strategy == "best"`.
+        # Should raise ValueError.
         with tempfile.TemporaryDirectory() as tmpdir:
             with self.assertRaises(ValueError) as context:
                 trainer = get_regression_trainer(
@@ -4232,9 +4234,22 @@ class TrainerIntegrationTest(TestCasePlus, TrainerIntegrationCommon):
                     save_strategy="best",
                     compute_metrics=AlmostAccuracy(),
                 )
-
             self.assertIn("`args.metric_for_best_model` must be provided", str(context.exception))
 
+        # Case 2: Metric name not provided when `load_best_model_at_end == True`.
+        # `metric_for_best_model` should be set to `"loss"` by default.
+        with tempfile.TemporaryDirectory() as tmpdir:
+            trainer = get_regression_trainer(
+                a=1.5,
+                b=2.5,
+                output_dir=tmpdir,
+                learning_rate=0.1,
+                eval_strategy="steps",
+                save_strategy="steps",
+                load_best_model_at_end=True,
+            )
+            self.assertTrue(trainer.args.metric_for_best_model == "loss")
+
 
 @require_torch
 @is_staging_test