Training with a custom service account needs a new field named service account
trainingInput:
  serviceAccount: CUSTOM_SERVICE_ACCOUNT

https://cloud.google.com/ai-platform/training/docs/custom-service-account


airflow/providers/google/cloud/operators/mlengine.py
"""
    Operator for launching a MLEngine training job.
    .. seealso::
        For more information on how to use this operator, take a look at the guide:
        :ref:`howto/operator:MLEngineStartTrainingJobOperator`
    :param job_id: A unique templated id for the submitted Google MLEngine
        training job. (templated)
    :type job_id: str
    :param package_uris: A list of package locations for MLEngine training job,
        which should include the main training program + any additional
        dependencies. (templated)
    :type package_uris: List[str]
    :param training_python_module: The Python module name to run within MLEngine
        training job after installing 'package_uris' packages. (templated)
    :type training_python_module: str
    :param training_args: A list of templated command line arguments to pass to
        the MLEngine training program. (templated)
    :type training_args: List[str]
    :param region: The Google Compute Engine region to run the MLEngine training
        job in (templated).
    :type region: str
    :param scale_tier: Resource tier for MLEngine training job. (templated)