\theta_{\psi_{k^{(i)}}(\mathfrak{j}_{\text{min}}^{(i,\ell)})}^{(i,\ell+0)} = \theta_{\psi_{k^{(i)}}(\mathfrak{j}_{\text{min}}^{(i,\ell)})}^{(i,\ell)} + \varepsilon_{\psi_{k^{(i)}}(\mathfrak{j}_{\text{min}}^{(i,\ell)})}^{(i,\ell)}