diff --git a/torch/distributed/optim/optimizer.py b/torch/distributed/optim/optimizer.py
index b10eacefea0..a68e9fc9c11 100644
--- a/torch/distributed/optim/optimizer.py
+++ b/torch/distributed/optim/optimizer.py
@@ -1,4 +1,5 @@
 from typing import List, Optional
+import logging
 
 import torch.distributed.rpc as rpc
 import torch.optim as optim
@@ -18,6 +19,7 @@ import torch.distributed.autograd as dist_autograd
 from collections import defaultdict
 from threading import Lock
 
+logger = logging.getLogger(__name__)
 
 # XXX: we define a _ScriptModuleOptimizer here to explicitly
 # compile the FunctionalOptimizer class into TorchScript
@@ -207,6 +209,13 @@ class DistributedOptimizer:
         if self.is_functional_optim:
             optimizer_new_func = _new_script_local_optimizer
         else:
+            logger.warn(
+                f"Creating the optimizer {optimizer_class} without TorchScript support, "
+                "this might result in slow computation time in multithreading environment"
+                "(i.e. Distributed Model Parallel training on CPU) due to the Python's "
+                "Global Interpreter Lock (GIL). Please file an issue if you need this "
+                "optimizer in TorchScript. "
+            )
             optimizer_new_func = _new_local_optimizer
 
         remote_optim_futs = []