This paper develops local certificates for population-risk increments around a current model. For a local candidate set $\mathcal D$, the certificate is a two-sided confidence band for $P({\ell_{θ+v}-\ell_θ})$ over $v\in\mathcal D$.

As an application, the upper endpoint of this band yields a risk-controlled update rule: an update is accepted only when its certified upper endpoint is nonpositive; otherwise the current model is retained.