code: def test(self, scheduler_type, optimizer_type):
      def _my_lambda(epoch):
          return epoch // 10
  
      def _optimizer_callable(params) -> Optimizer:
          return torch.optim.AdamW(params=params)
  
      def _lr_scheduler_callable(optimizer) -> _LRScheduler:
          return LambdaLR(optimizer, _my_lambda)
  
      hidden_dim = 10
      model = SimpleModel(hidden_dim)
  
      config_dict = {"train_batch_size": 1}
  
      client_optimizer = None
      client_scheduler = None
  
      if optimizer_type is None:
          config_dict["optimizer"] = {"type": ADAM_OPTIMIZER}
      elif optimizer_type is Optimizer:
          client_optimizer = torch.optim.Adam(model.parameters())
      else:
          client_optimizer = _optimizer_callable
  
      if scheduler_type is None:
          config_dict["scheduler"] = {"type": WARMUP_LR, "params": {}}
      elif scheduler_type == _LRScheduler:
          if isinstance(client_optimizer, Optimizer):
              client_scheduler = LambdaLR(client_optimizer, _my_lambda)
          else:
              # Verify invalid combination is correctly handled
              client_scheduler = LambdaLR(
                  torch.optim.Adam(model.parameters()), _my_lambda
              )
      else:
          client_scheduler = _lr_scheduler_callable
  
      if isinstance(client_scheduler, _LRScheduler) and not isinstance(
          client_optimizer, Optimizer
      ):
          with pytest.raises(AssertionError):
              _, _, _, _ = deepspeed.initialize(
                  config=config_dict,
                  model=model,
                  model_parameters=list(model.parameters()),
                  optimizer=client_optimizer,
                  lr_scheduler=client_scheduler,
              )
      else:
          _, _, _, ds_lr_scheduler = deepspeed.initialize(
              config=config_dict,
              model=model,
              model_parameters=list(model.parameters()),
              optimizer=client_optimizer,
              lr_scheduler=client_scheduler,
          )
          if client_scheduler is None:
              assert isinstance(ds_lr_scheduler, WarmupLR)
          elif isinstance(client_scheduler, _LRScheduler):
              assert ds_lr_scheduler == client_scheduler
          else:
              assert isinstance(ds_lr_scheduler, LambdaLR)
  
imports: import pytest
  from typing import Callable
  import torch
  from torch.optim import Optimizer, Adam, AdamW
  from torch.optim.lr_scheduler import _LRScheduler, LambdaLR
  from unit.simple_model import SimpleModel, random_dataloader
  from unit.common import DistributedTest
  from unit.util import bf16_required_version_check, required_amp_check
  import deepspeed
  from deepspeed.ops.adam import FusedAdam
  from deepspeed.runtime.lr_schedules import WARMUP_LR, WarmupLR
  from deepspeed.runtime.config import ADAM_OPTIMIZER
  from deepspeed.runtime.utils import see_memory_usage, required_torch_version
label_desc: Use image node_id 1 for calling the TestClientLrScheduler obj's underlying member method code with example usage: obj.test(scheduler_type, optimizer_type) and returns: unknown, torch, LambdaLR