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

2025-12-16

AI Summary

This paper addresses the deployment of multiclass classification under system-level linear constraints—such as fairness, reject-option policies, and user churn control. We propose a general, retraining-free post-processing framework that models constraints as linear functionals over randomized classifiers and solves them via entropy regularization and dual optimization. Our approach is the first to achieve unified, provably feasible randomized multiclass post-calibration for arbitrary systems of linear constraints. Theoretical analysis establishes finite-sample upper bounds on classification risk while guaranteeing exact constraint satisfaction. The method operates solely on the outputs of the pre-trained classifier and, under minimal assumptions, simultaneously ensures controllable performance and strict constraint adherence. This significantly enhances practicality and generalizability for constrained deployment in industrial settings.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• Adjusts base classifiers to meet system constraints without retraining
• Formulates as constrained stochastic program using entropic regularization
• Ensures risk and constraint satisfaction with finite-sample guarantees

Innovation

• Post-processing adjusts base classifier for constraints
• Uses entropic regularization and dual optimization techniques
• Accommodates fairness, abstention, and churn requirements