  Here is the Python code based on the given instructions:
```python
import torch
import torch.nn as nn
import torch.optim as optim
import torch.distributed as dist
import torchrec as trec

def _get_random_dataloader(num_embeddings, batch_size, pin_memory):
    # Create a random dataset
    dataset = torch.randn(num_embeddings, 10)

    # Create a DataLoader object
    dataloader = torch.utils.data.DataLoader(dataset, batch_size=batch_size, pin_memory=pin_memory)

    return dataloader

def train(num_embeddings, embedding_dim, dense_layer_sizes, over_layer_sizes, learning_rate):
    # Initialize the process group, device, rank, and backend
    dist.init_process_group(backend='nccl')
    device = torch.device('cuda')
    rank = dist.get_rank()
    backend = dist.Backend.NCCL

    # Construct a DLRM model
    model = trec.DLRM(num_embeddings, embedding_dim, dense_layer_sizes, over_layer_sizes)

    # Enable optimizer fusion
    model.enable_optimizer_fusion()

    # Distribute the model across devices
    model = model.to(device)

    # Overlap communication, compute, and device transfer during training
    model.overlap_communication_and_compute()

    # Initialize the optimizer
    optimizer = optim.SGD(model.parameters(), lr=learning_rate)

    # Create a training iterator
    dataloader = _get_random_dataloader(num_embeddings, 32, True)
    training_iterator = torch.utils.data.DataLoader(dataloader, batch_size=32, shuffle=True)

    # Train the model
    for epoch in range(10):
        for batch in training_iterator:
            # Compute the loss
            loss = model(batch)

            # Backpropagate the loss
            optimizer.zero_grad()
            loss.backward()

            # Update the model parameters
            optimizer.step()

    # Clean up the process group
    dist.destroy_process_group()

if __name__ == '__main__':
    train(1000, 10, [10, 10], [10, 10], 0.01)
```