I have two sequence prediction tasks, finding $\vec{\pi} \in \Pi$ and $\vec{\psi} \in \Psi$. Each sequence has its own objective function, i.e. $f_1(\vec{\pi})$ and $f_2(\vec{\psi})$. The input for the two sequence prediction tasks are also of different domain.
Say that by modification and extension in the model design, I can use one seq2seq or Pointer Network (or its variants) to produce the two sequence one at a time. In the training stage, however, the two objective functions are combined into $F(\vec{\pi}, \vec{\psi}) = \alpha f_1(\vec{\pi}) + \beta f_2(\vec{\psi})$ and the loss function to train the model use the combined objective function $F(\vec{\pi}, \vec{\psi})$.
Is this considered multi-task learning?
