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

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.

💡 Research Summary

This paper presents a unified post-processing framework for multi-class classification under system-level constraints. The core problem is to adjust the predictions of a pre-trained base classifier to satisfy a set of linear expectation-based constraints—such as fairness metrics, abstention rates, or churn limits—without requiring model retraining.

The authors formalize the task as a constrained stochastic program over randomized classifiers. A randomized classifier π is defined as a conditional distribution over an action set A (e.g., class labels or a reject action) given a feature vector X. The goal is to find a π that minimizes the expected loss E_π