diff --git a/pytorch_lightning/trainer/trainer.py b/pytorch_lightning/trainer/trainer.py
index f7f7eff35997f..9d462ef8f36aa 100644
--- a/pytorch_lightning/trainer/trainer.py
+++ b/pytorch_lightning/trainer/trainer.py
@@ -766,8 +766,16 @@ def use_type(x):
                 use_type = arg_types[0]
 
             if arg == 'gpus' or arg == 'tpu_cores':
-                use_type = Trainer._allowed_type
-                arg_default = Trainer._arg_default
+                use_type = Trainer._gpus_allowed_type
+                arg_default = Trainer._gpus_arg_default
+
+            # hack for types in (int, float)
+            if len(arg_types) == 2 and int in set(arg_types) and float in set(arg_types):
+                use_type = Trainer._int_or_float_type
+
+            # hack for track_grad_norm
+            if arg == 'track_grad_norm':
+                use_type = float
 
             parser.add_argument(
                 f'--{arg}',
@@ -780,18 +788,24 @@ def use_type(x):
 
         return parser
 
-    def _allowed_type(x) -> Union[int, str]:
+    def _gpus_allowed_type(x) -> Union[int, str]:
         if ',' in x:
             return str(x)
         else:
             return int(x)
 
-    def _arg_default(x) -> Union[int, str]:
+    def _gpus_arg_default(x) -> Union[int, str]:
         if ',' in x:
             return str(x)
         else:
             return int(x)
 
+    def _int_or_float_type(x) -> Union[int, float]:
+        if '.' in str(x):
+            return float(x)
+        else:
+            return int(x)
+
     @classmethod
     def parse_argparser(cls, arg_parser: Union[ArgumentParser, Namespace]) -> Namespace:
         """Parse CLI arguments, required for custom bool types."""