Randomized multi-class classification under system constraints: a unified approach via post-processing

TL;DR

This paper introduces a unified post-processing method for multi-class classification that adjusts classifiers to meet diverse system constraints like fairness and abstention without retraining, using a stochastic programming approach with guarantees.

Contribution

It presents a novel framework that formulates constrained classification as a linearly constrained stochastic program, enabling flexible constraint satisfaction with theoretical guarantees.

Findings

Effective adjustment of classifiers to meet constraints

Finite-sample guarantees for risk and constraint satisfaction

Framework accommodates various constraints such as fairness and abstention

Abstract

We study the problem of multi-class classification under system-level constraints expressible as linear functionals over randomized classifiers. We propose a post-processing approach that adjusts a given base classifier to satisfy general constraints without retraining. Our method formulates the problem as a linearly constrained stochastic program over randomized classifiers, and leverages entropic regularization and dual optimization techniques to construct a feasible solution. We provide finite-sample guarantees for the risk and constraint satisfaction for the final output of our algorithm under minimal assumptions. The framework accommodates a broad class of constraints, including fairness, abstention, and churn requirements.