Optimizing Generalized Rate Metrics with Three Players

Harikrishna Narasimhan‎, Andrew Cotter, Maya Gupta

Abstract: We present a three-player game approach for solving a large class of learning problems with general 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 nonlinear 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 nonlinear rate constraints. We provide convergence guarantees for convex functions of rates, and show how our algorithms can be extended to handle sums of ratios of rates. Experiments on different fairness tasks confirm the efficacy of our approach.

CMT Num: 5730

Code Link: https://github.com/google-research/google-research/tree/master/generalized_rates