A Family of Convex Models to Achieve Fairness through Dispersion Control
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910219968184320 |
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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 |
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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 |