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,
        *,
        model: dict,
        operation: str = 'create',
        project_id: Optional[str] = None,
        gcp_conn_id: str = 'google_cloud_default',
        delegate_to: Optional[str] = None,
        impersonation_chain: Optional[Union[str, Sequence[str]]] = None,
        **kwargs,
    ) -> None:
        super().__init__(**kwargs)
        warnings.warn(
            "This operator is deprecated. Consider using operators for specific operations: "
            "MLEngineCreateModelOperator, MLEngineGetModelOperator.",
            DeprecationWarning,
            stacklevel=3,
        )
        self._project_id = project_id
        self._model = model
        self._operation = operation
        self._gcp_conn_id = gcp_conn_id
        self._delegate_to = delegate_to
        self._impersonation_chain = impersonation_chain
    def execute(self, context):