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
self,  
        *,
        job_id: str,
        package_uris: List[str],
        training_python_module: str,
        training_args: List[str],
        region: str,
        scale_tier: Optional[str] = None,
        master_type: Optional[str] = None,
        master_config: Optional[Dict] = None,
        runtime_version: Optional[str] = None,
        python_version: Optional[str] = None,
        job_dir: Optional[str] = None,
        project_id: Optional[str] = None,
        gcp_conn_id: str = 'google_cloud_default',
        delegate_to: Optional[str] = None,
        mode: str = 'PRODUCTION',
        labels: Optional[Dict[str, str]] = None,
        impersonation_chain: Optional[Union[str, Sequence[str]]] = None,
        **kwargs,
    ) -> None:
        super().__init__(**kwargs)
        self._project_id = project_id
        self._job_id = job_id
        self._package_uris = package_uris
        self._training_python_module = training_python_module