def get_tuning_keys(tuning_space: dict):
    """Outputs the list of tunnable parameters in the tuning space dict.

    Args:
        tuning_space (dict): a configuration dictionary containing tunable parameters as lists of values.

    Returns:
        A list of strings
    """
    tuning_keys = []
    for key, val in tuning_space.items():
        if isinstance(val, dict):
            tuning_keys.extend(get_tuning_keys(val))
        if isinstance(val, list) and len(val) > 1:
            tuning_keys.append(key)
    return tuning_keys