# Consistent Multiclass Algorithms for Complex Metrics and Constraints

arXiv: https://arxiv.org/abs/2210.09695 · HTML: https://mlsanity.com/paper/2210.09695/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2022.

## Built on by (most cited first, 13 of 13)

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- [Establishing Linear Surrogate Regret Bounds for Convex Smooth Losses via Convolutional Fenchel-Young Losses](https://mlsanity.com/paper/2505.09432/) (2025)
- [Randomized multi-class classification under system constraints: a unified approach via post-processing](https://mlsanity.com/paper/2512.14246/) (2025)
- [An Efficient Plugin Method for Metric Optimization of Black-Box Models](https://mlsanity.com/paper/2503.02119/) (2025)
- [Optimizing Shortfall Risk Metric for Learning Regression Models](https://mlsanity.com/paper/2505.17777/) (2025)
- [FedFACT: A Provable Framework for Controllable Group-Fairness Calibration in Federated Learning](https://mlsanity.com/paper/2506.03777/) (2025)
- [Imbalanced Classification under Capacity Constraints](https://mlsanity.com/paper/2605.03289/) (2026)
- [Principled Algorithms for Optimizing Generalized Metrics in Multi-Label Learning](https://mlsanity.com/paper/2605.28767/) (2026)
- [Demystifying the Optimal Fair Classifier in Multi-Class Classification](https://mlsanity.com/paper/2606.00656/) (2026)

## Abstract (arXiv)

We present consistent algorithms for multiclass learning with complex performance metrics and constraints, where the objective and constraints are defined by arbitrary functions of the confusion matrix. This setting includes many common performance metrics such as the multiclass G-mean and micro F1-measure, and constraints such as those on the classifier's precision and recall and more recent measures of fairness discrepancy. We give a general framework for designing consistent algorithms for such complex design goals by viewing the learning problem as an optimization problem over the set of feasible confusion matrices. We provide multiple instantiations of our framework under different assumptions on the performance metrics and constraints, and in each case show rates of convergence to the optimal (feasible) classifier (and thus asymptotic consistency). Experiments on a variety of multiclass classification tasks and fairness-constrained problems show that our algorithms compare favorably to the state-of-the-art baselines.