A Family of Convex Models to Achieve Fairness through Dispersion Control

Fuente: arXiv
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Main Authors: Bhadoriya, Abhay Singh, Deka, Deepjyoti, Sundar, Kaarthik
Format: Preprint
Published: 2025
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author Bhadoriya, Abhay Singh
Deka, Deepjyoti
Sundar, Kaarthik
author_facet Bhadoriya, Abhay Singh
Deka, Deepjyoti
Sundar, Kaarthik
contents Controlling the dispersion of a subset of decision variables in an optimization problem is crucial for enforcing fairness or load-balancing across a wide range of applications. Building on the well-known equivalence of finite-dimensional norms, the article develops a family of parameterized convex models that regulate the dispersion of a vector of decision-variable values through its coefficient of variation. Each model has a single parameter taking values in the interval $[0,1]$. When the parameter is set to zero, the model imposes only a trivial constraint on the optimization problem; when set to one, it enforces equality of all the decision variables. As the parameter varies, the coefficient of variation is provably bounded above by a monotonic function of that parameter. The article also presents theoretical results relating the space of feasible solutions across all models. Finally, it compares the models' solution quality on a variant of the assignment problem that regulates the dispersion in the assignment costs.
format Preprint
id arxiv_https___arxiv_org_abs_2510_23791
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Family of Convex Models to Achieve Fairness through Dispersion Control
Bhadoriya, Abhay Singh
Deka, Deepjyoti
Sundar, Kaarthik
Optimization and Control
Controlling the dispersion of a subset of decision variables in an optimization problem is crucial for enforcing fairness or load-balancing across a wide range of applications. Building on the well-known equivalence of finite-dimensional norms, the article develops a family of parameterized convex models that regulate the dispersion of a vector of decision-variable values through its coefficient of variation. Each model has a single parameter taking values in the interval $[0,1]$. When the parameter is set to zero, the model imposes only a trivial constraint on the optimization problem; when set to one, it enforces equality of all the decision variables. As the parameter varies, the coefficient of variation is provably bounded above by a monotonic function of that parameter. The article also presents theoretical results relating the space of feasible solutions across all models. Finally, it compares the models' solution quality on a variant of the assignment problem that regulates the dispersion in the assignment costs.
title A Family of Convex Models to Achieve Fairness through Dispersion Control
topic Optimization and Control
url https://arxiv.org/abs/2510.23791