  Only recently, researchers attempt to provide classification algorithms with
provable group fairness guarantees. Most of these algorithms suffer from
harassment caused by the requirement that the training and deployment data
follow the same distribution. This paper proposes an input-agnostic certified
group fairness algorithm, FairSmooth, for improving the fairness of
classification models while maintaining the remarkable prediction accuracy. A
Gaussian parameter smoothing method is developed to transform base classifiers
into their smooth versions. An optimal individual smooth classifier is learnt
for each group with only the data regarding the group and an overall smooth
classifier for all groups is generated by averaging the parameters of all the
individual smooth ones. By leveraging the theory of nonlinear functional
analysis, the smooth classifiers are reformulated as output functions of a
Nemytskii operator. Theoretical analysis is conducted to derive that the
Nemytskii operator is smooth and induces a Frechet differentiable smooth
manifold. We theoretically demonstrate that the smooth manifold has a global
Lipschitz constant that is independent of the domain of the input data, which
derives the input-agnostic certified group fairness.
