Set `run_name` in MLflowCallback (#14894)

* Set run_name in MLflowCallback

* Update the docs for `run_name` argument

src/transformers/integrations.py

@@ -712,7 +712,7 @@ class MLflowCallback(TrainerCallback):
         if log_artifacts in {"TRUE", "1"}:
             self._log_artifacts = True
         if state.is_world_process_zero:
-            self._ml_flow.start_run()
+            self._ml_flow.start_run(run_name=args.run_name)
             combined_dict = args.to_dict()
             if hasattr(model, "config") and model.config is not None:
                 model_config = model.config.to_dict()

src/transformers/training_args.py

@@ -256,7 +256,7 @@ class TrainingArguments:
             `Trainer` will use the corresponding output (usually index 2) as the past state and feed it to the model
             at the next training step under the keyword argument `mems`.
         run_name (`str`, *optional*):
-            A descriptor for the run. Typically used for [wandb](https://www.wandb.com/) logging.
+            A descriptor for the run. Typically used for [wandb](https://www.wandb.com/) and [mlflow](https://www.mlflow.org/) logging.
         disable_tqdm (`bool`, *optional*):
             Whether or not to disable the tqdm progress bars and table of metrics produced by
             [`~notebook.NotebookTrainingTracker`] in Jupyter Notebooks. Will default to `True`