Optimizing Generalized Rate Metrics through Game Equilibrium
This provides a general solution for machine learning practitioners needing to handle complex performance metrics or fairness constraints, though it builds incrementally on existing game-based methods.
The paper tackles the problem of optimizing non-linear functions of classification rates, such as F-measure or fairness constraints, by proposing a three-player game framework to decouple classifier rates from the objective, and demonstrates its efficacy through experiments on fairness tasks.
We present a general framework for solving a large class of learning problems with non-linear functions of classification rates. This includes problems where one wishes to optimize a non-decomposable performance metric such as the F-measure or G-mean, and constrained training problems where the classifier needs to satisfy non-linear rate constraints such as predictive parity fairness, distribution divergences or churn ratios. We extend previous two-player game approaches for constrained optimization to a game between three players to decouple the classifier rates from the non-linear objective, and seek to find an equilibrium of the game. Our approach generalizes many existing algorithms, and makes possible new algorithms with more flexibility and tighter handling of non-linear rate constraints. We provide convergence guarantees for convex functions of rates, and show how our methodology can be extended to handle sums of ratios of rates. Experiments on different fairness tasks confirm the efficacy of our approach.