This is where we deviate from what is common in machine learning. Rather than defining a cost function based on some dataset, our cost function is the energy of the quantum mechanical system. From the variational principle we know that minimizing this energy should lead to the ground state wavefunction. As stated previously the local energy is given by
$$ \begin{align*} E_L = \frac{1}{\Psi} \hat{\mathbf{H}} \Psi. \end{align*} $$