[logging] Fix race condition in LoggerHandler during multi-GPU training (#10156)

Co-authored-by: yurekami <yurekami@users.noreply.github.com>

src/llamafactory/extras/logging.py

@@ -41,12 +41,13 @@ class LoggerHandler(logging.Handler):
             datefmt="%Y-%m-%d %H:%M:%S",
         )
         self.setLevel(logging.INFO)
+        self.thread_pool = ThreadPoolExecutor(max_workers=1)
         os.makedirs(output_dir, exist_ok=True)
         self.running_log = os.path.join(output_dir, RUNNING_LOG)
-        if os.path.exists(self.running_log):
+        try:
             os.remove(self.running_log)
-
-        self.thread_pool = ThreadPoolExecutor(max_workers=1)
+        except OSError:
+            pass
 
     def _write_log(self, log_entry: str) -> None:
         with open(self.running_log, "a", encoding="utf-8") as f: