ale parameter is set such that given
the exact MLE
$$\hat{g} := \mathrm{argmax}_{g \in G} L(g),$$
where \(G\) is the full nonparametric family, and given the MLE for the
approximating family \(\tilde{G}\)
$$\tilde{g} := \mathrm{argmax}_{g \in \tilde{G}} L(g),$$
we have that
$$\mathrm{KL}(\hat{g} \ast N(0, s^2) \mid \tilde{g} \ast N(0, s^2)) \le \kappa,$$
where \(\ast \ N(0, s^2)\) denotes convolution with the normal error
distribution (the derivation of the bound assumes homoskedastic
observations). For det