  We consider the problem of producing fair probabilistic classifiers for
multi-class classification tasks. We formulate this problem in terms of
"projecting" a pre-trained (and potentially unfair) classifier onto the set of
models that satisfy target group-fairness requirements. The new, projected
model is given by post-processing the outputs of the pre-trained classifier by
a multiplicative factor. We provide a parallelizable iterative algorithm for
computing the projected classifier and derive both sample complexity and
convergence guarantees. Comprehensive numerical comparisons with
state-of-the-art benchmarks demonstrate that our approach maintains competitive
performance in terms of accuracy-fairness trade-off curves, while achieving
favorable runtime on large datasets. We also evaluate our method at scale on an
open dataset with multiple classes, multiple intersectional protected groups,
and over 1M samples.
