code: def test_optimizer_for_hierarchical_model(
      device, communication_type, kwargs
  ):
      atc_style = kwargs.get("ATC", False)
      error_threshold = kwargs.get("error_threshold", 1.5)
      window_prefix = kwargs.get("window_prefix", None)
  
      (
          problem_builder,
          train_dataloader,
          test_dataloader,
          model,
          optimizer,
          num_epochs,
      ) = problem_setup(HierarchicalLinearNet)
  
      isCUDA = pin_model_to_device(device, model)
  
      if isinstance(communication_type, bf.CommunicationType):
          base_dist_optimizer = (
              bf.DistributedAdaptThenCombineOptimizer
              if atc_style
              else bf.DistributedAdaptWithCombineOptimizer
          )
          optimizer = base_dist_optimizer(
              optimizer,
              model=model,
              communication_type=communication_type,
          )
      elif communication_type == "win.put":
          optimizer = bf.DistributedWinPutOptimizer(
              optimizer, model=model, window_prefix=window_prefix
          )
      elif communication_type == "gradient.allreduce":
          optimizer = bf.DistributedGradientAllreduceOptimizer(
              optimizer, model=model
          )
      else:
          raise ValueError(
              "Communication_type under test is not expected."
          )
  
      # Train and test
      train_mse = []
      test_mse = []
      for _ in range(num_epochs):
          standard_train(model, optimizer, train_dataloader, isCUDA)
          train_mse.append(evaluation(model, train_dataloader, isCUDA))
          test_mse.append(evaluation(model, test_dataloader, isCUDA))
      train_mse = np.array(train_mse)
      test_mse = np.array(test_mse)
  
      # Check if the MSEs in the last three epochs are small enough
      assert (
          train_mse[-3:].max()
          < error_threshold * problem_builder.noise_level**2
      ), "Train MSE in the last three epochs doesn't coverge."
      assert (
          test_mse[-3:].max()
          < error_threshold * problem_builder.noise_level**2
      ), "Train MSE in the last three epochs doesn't coverge."
  
      if communication_type == "win.put":
          optimizer.unregister_window()
  
imports: from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  import pytest
  import numpy
  import torch
  import torch.nn
  import torch.optim
  from torch.utils.data import Dataset, DataLoader
  import bluefog.torch
  from bluefog.common import topology_util
label_desc: Use image node_id 9 for calling a global function with example usage: test_optimizer_for_hierarchical_model(device, communication_type, kwargs) without return types