questions about bi-level optimization in prior matching loss

[KennyNH]

Hi.

As can be seen in paper, the prior matching is a bi-level optimization problem. For params of encoder, we should maximize the objective, while we should minimize it for params of discriminator (in prior matching). However, the prior loss is just added as part of total loss, which means the objectives of two optimization problems are the same (i.e. maximization). Does this contradict to Eq. 7 in paper?