  Algorithmic fairness seeks to identify and correct sources of bias in machine
learning algorithms. Confoundingly, ensuring fairness often comes at the cost
of accuracy. We provide formal tools in this work for reconciling this
fundamental tension in algorithm fairness. Specifically, we put to use the
concept of Pareto optimality from multi-objective optimization and seek the
fairness-accuracy Pareto front of a neural network classifier. We demonstrate
that many existing algorithmic fairness methods are performing the so-called
linear scalarization scheme which has severe limitations in recovering Pareto
optimal solutions. We instead apply the Chebyshev scalarization scheme which is
provably superior theoretically and no more computationally burdensome at
recovering Pareto optimal solutions compared to the linear scheme.
