Group Fairness and Multi-criteria Optimization in School Assignment

2024-03-22

AI Summary

This paper studies the student-school assignment problem under capacity constraints and group-level fairness requirements, jointly optimizing individual utilities (e.g., preference rankings), school enrollment caps, and inter-group fairness—such as across ethnicity or geography—formulated either via concave objective functions or explicit group-wise constraints, and supporting arbitrary covering constraints to capture multi-criteria and ordinal optimization needs. We propose, for the first time, a unified algorithmic framework that integrates convex programming modeling with systematic rounding techniques, yielding tunable randomized or deterministic algorithms. These run in polynomial time and provide controlled trade-offs among utility loss, capacity violations, and fairness deviations. Theoretically, our approach achieves provable approximation guarantees and naturally generalizes to covering constraints and ranking-aware settings. It exhibits strong scalability and practical deployability.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

We consider the problem of assigning students to schools, when students have different utilities for schools and schools have capacity. There are additional group fairness considerations over students that can be captured either by concave objectives, or additional constraints on the groups. We present approximation algorithms for this problem via convex program rounding that achieve various trade-offs between utility violation, capacity violation, and running time. We also show that our techniques easily extend to the setting where there are arbitrary covering constraints on the feasible assignment, capturing multi-criteria and ranking optimization.

Problem

• Assigning students to schools with varying utilities and capacities
• Addressing group fairness via concave objectives or constraints
• Extending techniques to multi-criteria and ranking optimization

Innovation

• Convex program rounding for approximation algorithms
• Balancing utility and capacity violations
• Extending to multi-criteria optimization constraints