# Demystifying the Optimal Fair Classifier in Multi-Class Classification

arXiv: https://arxiv.org/abs/2606.00656 · HTML: https://mlsanity.com/paper/2606.00656/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 66 references that are in the map.
- First posted on arXiv 30 May 2026.

## Builds on (most cited first, 30 of 43)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [Long-tail learning via logit adjustment](https://mlsanity.com/paper/2007.07314/) (2020)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [FutureSightDrive: Thinking Visually with Spatio-Temporal CoT for Autonomous Driving](https://mlsanity.com/paper/2505.17685/) (2025)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [CelebA-Spoof: Large-Scale Face Anti-Spoofing Dataset with Rich Annotations](https://mlsanity.com/paper/2007.12342/) (2020)
- [Optimization with Non-Differentiable Constraints with Applications to Fairness, Recall, Churn, and Other Goals](https://mlsanity.com/paper/1809.04198/) (2018)
- [FairBatch: Batch Selection for Model Fairness](https://mlsanity.com/paper/2012.01696/) (2020)
- [JanusVLN: Decoupling Semantics and Spatiality with Dual Implicit Memory for Vision-Language Navigation](https://mlsanity.com/paper/2509.22548/) (2025)
- [Fairlearn: Assessing and Improving Fairness of AI Systems](https://mlsanity.com/paper/2303.16626/) (2023)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [NeuronFair: Interpretable White-Box Fairness Testing through Biased Neuron Identification](https://mlsanity.com/paper/2112.13214/) (2021)
- [ReMasker: Imputing Tabular Data with Masked Autoencoding](https://mlsanity.com/paper/2309.13793/) (2023)
- [FFB: A Fair Fairness Benchmark for In-Processing Group Fairness Methods](https://mlsanity.com/paper/2306.09468/) (2023)
- [Learning fair representation with a parametric integral probability metric](https://mlsanity.com/paper/2202.02943/) (2022)
- [Re-weighting Based Group Fairness Regularization via Classwise Robust Optimization](https://mlsanity.com/paper/2303.00442/) (2023)
- [FRAPPE: A Group Fairness Framework for Post-Processing Everything](https://mlsanity.com/paper/2312.02592/) (2023)
- [The Fairness of Credit Scoring Models](https://mlsanity.com/paper/2205.10200/) (2022)
- [Multi-class SVMs: From Tighter Data-Dependent Generalization Bounds to Novel Algorithms](https://mlsanity.com/paper/1506.04359/) (2015)
- [Post-hoc Bias Scoring Is Optimal For Fair Classification](https://mlsanity.com/paper/2310.05725/) (2023)
- [Fair Risk Control: A Generalized Framework for Calibrating Multi-group Fairness Risks](https://mlsanity.com/paper/2405.02225/) (2024)
- [Multi-Modal Multi-Behavior Sequential Recommendation with Conditional Diffusion-Based Feature Denoising](https://mlsanity.com/paper/2508.05352/) (2025)

## Abstract (arXiv)

Ensuring fair and equitable treatment across diverse groups, particularly in multi-class classification tasks, poses a significant challenge due to the persistent biases inherent in machine learning models. Most existing bias mitigation techniques are tailored to binary settings, and the presence of multi-dimensional outputs and complex fairness mechanisms makes their extension to multi-class scenarios neither straightforward nor effective. In this paper, we investigate two fundamental, unresolved challenges in fair classification: (i) characterizing the optimal accuracy-fairness frontier in multi-class settings, and (ii) designing practical algorithms that attain this optimum in different training phases. To tackle these challenges, we first specify an analytically tractable probabilistic formulation of the optimal classifier under fairness constraints. Building upon this, we propose two attribute-blind algorithms to enforce fairness requirements in practice: an in-processing approach for fairness intervention during training via the reduction approach, and a post-processing approach for fine-tuning output probabilities with plug-in estimation. Theoretical analysis reveals that both methods converge to the optimal accuracy-fairness Pareto frontier. Experiments conducted on multiple datasets demonstrate the superior performance of our methods in balancing accuracy and fairness.