Bi-Level Optimization#

\[\begin{split} \begin{aligned} \boldsymbol{\theta}^* &= \underset{\boldsymbol{\theta}}{\text{argmax}} \hspace{2mm} \mathcal{L}(\boldsymbol{\theta}) \\ \mathbf{u}^*(\boldsymbol{\theta}) &= \underset{\mathbf{u}}{\text{argmax}} \hspace{2mm} \mathcal{J}(\mathbf{u};\boldsymbol{\theta}) \end{aligned} \end{split}\]