Constrained Optimization of Nonconvex Problems and its Applications in Fairness in Machine Learning

Abstract

Fairness is an important concern in machine learning. One way to characterize the problem is to minimize some objective function, representing a quantity like loss, under constraints that represent fairness conditions like demographic parity. Previous papers show how a two-player approach to optimizing the Lagrangian can be computationally efficient and provably converge to a good, constraint-satisfying solution on convex objective functions. This work analyzes the convergence of the two-player framework in previous works on nonconvex functions, in particular those that satisfy the PL inequality.