from tensorflow.python.summary import summary

                           (", ".join(OPTIMIZER_SUMMARIES), summ))
    if learning_rate is not None and learning_rate_decay_fn is not None:
      if global_step is None:
        raise ValueError("global_step is required for learning_rate_decay_fn.")
      lr = learning_rate_decay_fn(lr, global_step)
      if "learning_rate" in summaries:
        summary.scalar("learning_rate", lr)

    # Create optimizer, given specified parameters.
    if isinstance(optimizer, six.string_types):
      if lr is None:
        raise ValueError("Learning rate is None, but should be specified if "
