 ```python
from torchrec.distributed.data_parallel import DistributedDataParallel
from torchrec.distributed.sharding import OverlapCommunication
from torchrec.modules.embedding_modules import EmbeddingCollection, NamedEmbedding
from torchrec.modules.module_utils import make_named_param_groups
from torchrec.sparse.jagged_tensor import JaggedTensor, SparseTensor
from torchrec.sparse.jagged_tensor.ops import to_dense
from torchrec.sparse.module import SparseAttention, SparseFusedDNN
from torchrec.sparse.module_utils import make_named_param_groups
from torchrec.torch import Tensor
from torchrec.utils import get_activation_fn, get_device, get_rank, get_world_size, initialize_and_test_parameters, log_parameters, set_seed
from torch.utils.data import DataLoader, Dataset
from torch.nn import functional as F
from torch import nn
import torch
import os

def _get_random_dataloader(num_embeddings: int, batch_size: int, pin_memory: bool):
    class RandomDataset(Dataset):
        def __init__(self, num_embeddings, batch_size):
            self.num_embeddings = num_embeddings
            self.batch_size = batch_size

        def __getitem__(self, index):
            return torch.randint(0, self.num_embeddings, (self.batch_size,))

        def __len__(self):
            return 10000

    return DataLoader(RandomDataset(num_embeddings, batch_size), batch_size=batch_size, pin_memory=pin_memory)

def train(num_embeddings: int, embedding_dim: int, dense_arch: list[int], sparse_arch: list[int], learning_rate: float):
    set_seed(42)

    initialize_and_test_parameters()

    device = get_device()
    rank = get_rank()
    world_size = get_world_size()

    model = DLRMModel(num_embeddings, embedding_dim, dense_arch, sparse_arch).to(device)

    optimizer = torch.optim.AdamW(make_named_param_groups(model), lr=learning_rate)

    overlap_comm = OverlapCommunication(model, device, rank, world_size)

    train_iterator = _get_random_dataloader(num_embeddings, 128, False)

    for epoch in range(10):
        for batch in train_iterator:
            input_ids = batch.to(device)
            label = torch.randint(0, 2, (batch.shape[0],)).to(device)

            optimizer.zero_grad()

            output = model(input_ids)

            loss = F.binary_cross_entropy_with_logits(output, label)

            loss.backward()

            optimizer.step()

            overlap_comm.step()

if __name__ == '__main__':
    train(100000, 128, [256, 256], [128, 128], 0.001)
```

Note: The `DLRMModel` class is not implemented in this code. You can implement it based on the DLRM architecture.