# Loss Balancing for Fair Supervised Learning

arXiv: https://arxiv.org/abs/2311.03714 · HTML: https://mlsanity.com/paper/2311.03714/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 50 references that are in the map.
- First posted on arXiv 7 Nov 2023.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [Equity of Attention: Amortizing Individual Fairness in Rankings](https://mlsanity.com/paper/1805.01788/) (2018)
- [FairBatch: Batch Selection for Model Fairness](https://mlsanity.com/paper/2012.01696/) (2020)
- [Fairness risk measures](https://mlsanity.com/paper/1901.08665/) (2019)
- [Group Retention when Using Machine Learning in Sequential Decision Making: the Interplay between User Dynamics and Fairness](https://mlsanity.com/paper/1905.00569/) (2019)
- [Individual Fairness in Hindsight](https://mlsanity.com/paper/1812.04069/) (2018)
- [Optimising Equal Opportunity Fairness in Model Training](https://mlsanity.com/paper/2205.02393/) (2022)
- [An Algorithmic Framework for Fairness Elicitation](https://mlsanity.com/paper/1905.10660/) (2019)
- [Improving Fairness and Privacy in Selection Problems](https://mlsanity.com/paper/2012.03812/) (2020)
- [Fair Sequential Selection Using Supervised Learning Models](https://mlsanity.com/paper/2110.13986/) (2021)
- [Towards Learning an Unbiased Classifier from Biased Data via Conditional Adversarial Debiasing](https://mlsanity.com/paper/2103.06179/) (2021)
- [Symbolic Metamodels for Interpreting Black-boxes Using Primitive Functions](https://mlsanity.com/paper/2302.04791/) (2023)

## Built on by (most cited first, 11 of 11)

- [15M Multimodal Facial Image-Text Dataset](https://mlsanity.com/paper/2407.08515/) (2024)
- [Addressing Polarization and Unfairness in Performative Prediction](https://mlsanity.com/paper/2406.16756/) (2024)
- [Counterfactually Fair Representation](https://mlsanity.com/paper/2311.05420/) (2023)
- [Improved Balanced Classification with Theoretically Grounded Loss Functions](https://mlsanity.com/paper/2512.23947/) (2025)
- [The Statistical Fairness-Accuracy Frontier](https://mlsanity.com/paper/2508.17622/) (2025)
- [Lookahead Counterfactual Fairness](https://mlsanity.com/paper/2412.01065/) (2024)
- [Meta Optimality for Demographic Parity Constrained Regression via Post-Processing](https://mlsanity.com/paper/2506.13947/) (2025)
- [Demographic-Agnostic Fairness without Harm](https://mlsanity.com/paper/2509.24077/) (2025)
- [Achieving Fairness Without Harm via Selective Demographic Experts](https://mlsanity.com/paper/2511.06293/) (2025)
- [Benchmarking Bias Mitigation Toward Fairness Without Harm from Vision to LVLMs](https://mlsanity.com/paper/2602.03895/) (2026)
- [A Critical Review of Predominant Bias in Neural Networks](https://mlsanity.com/paper/2502.11031/) (2025)

## Abstract (arXiv)

Supervised learning models have been used in various domains such as lending, college admission, face recognition, natural language processing, etc. However, they may inherit pre-existing biases from training data and exhibit discrimination against protected social groups. Various fairness notions have been proposed to address unfairness issues. In this work, we focus on Equalized Loss (EL), a fairness notion that requires the expected loss to be (approximately) equalized across different groups. Imposing EL on the learning process leads to a non-convex optimization problem even if the loss function is convex, and the existing fair learning algorithms cannot properly be adopted to find the fair predictor under the EL constraint. This paper introduces an algorithm that can leverage off-the-shelf convex programming tools (e.g., CVXPY) to efficiently find the global optimum of this non-convex optimization. In particular, we propose the ELminimizer algorithm, which finds the optimal fair predictor under EL by reducing the non-convex optimization to a sequence of convex optimization problems. We theoretically prove that our algorithm finds the global optimal solution under certain conditions. Then, we support our theoretical results through several empirical studies.