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