We present a consistent algorithm for constrained classification problems where the objective (e.g. F-measure, G-mean) and the constraints (e.g. demographic parity fairness, coverage) are defined by general functions of the confusion matrix. Our approach reduces the problem into a sequence of plug-in classifier learning tasks. The reduction is achieved by posing the learning problem as an optimization over the intersection of two sets: the set of confusion matrices that are achievable and those that are feasible. This decoupling of the constraint space then allows us to solve the problem by applying Frank-Wolfe style optimization over the individual sets. For objective and constraints that are convex functions of the confusion matrix, our algorithm requires O(1/✏ 2 ) calls to the plug-in subroutine, which improves on the O(1/✏ 3 ) calls needed by the reduction-based algorithm of Narasimhan (2018) . We show empirically that our algorithm is competitive with prior methods,while being more robust to choices of hyper-parameters.