# A Unified Framework for Rank-based Loss Minimization

arXiv: https://arxiv.org/abs/2310.17237 · HTML: https://mlsanity.com/paper/2310.17237/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2023.

## Built on by (most cited first, 3 of 3)

- [QAMRO: Quality-aware Adaptive Margin Ranking Optimization for Human-aligned Assessment of Audio Generation Systems](https://mlsanity.com/paper/2508.08957/) (2025)
- [SOREL: A Stochastic Algorithm for Spectral Risks Minimization](https://mlsanity.com/paper/2407.14618/) (2024)
- [Convergence of empirical subgradients for optimal transport-based objectives](https://mlsanity.com/paper/2605.28134/) (2026)

## Abstract (arXiv)

The empirical loss, commonly referred to as the average loss, is extensively utilized for training machine learning models. However, in order to address the diverse performance requirements of machine learning models, the use of the rank-based loss is prevalent, replacing the empirical loss in many cases. The rank-based loss comprises a weighted sum of sorted individual losses, encompassing both convex losses like the spectral risk, which includes the empirical risk and conditional value-at-risk, and nonconvex losses such as the human-aligned risk and the sum of the ranked range loss. In this paper, we introduce a unified framework for the optimization of the rank-based loss through the utilization of a proximal alternating direction method of multipliers. We demonstrate the convergence and convergence rate of the proposed algorithm under mild conditions. Experiments conducted on synthetic and real datasets illustrate the effectiveness and efficiency of the proposed algorithm.