# A Tunable Loss Function for Binary Classification

arXiv: https://arxiv.org/abs/1902.04639 · HTML: https://mlsanity.com/paper/1902.04639/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2019.

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

- [Being Properly Improper](https://mlsanity.com/paper/2106.09920/) (2021)
- [Realizing GANs via a Tunable Loss Function](https://mlsanity.com/paper/2106.05232/) (2021)
- [Asymmetry of the Relative Entropy in the Regularization of Empirical Risk Minimization](https://mlsanity.com/paper/2410.02833/) (2024)
- [α-GAN: Convergence and Estimation Guarantees](https://mlsanity.com/paper/2205.06393/) (2022)
- [Analysis of the Relative Entropy Asymmetry in the Regularization of Empirical Risk Minimization](https://mlsanity.com/paper/2306.07123/) (2023)
- [Addressing GAN Training Instabilities via Tunable Classification Losses](https://mlsanity.com/paper/2310.18291/) (2023)
- [Proper losses regret at least 1/2-order](https://mlsanity.com/paper/2407.10417/) (2024)
- [(αD,αG)-GANs: Addressing GAN Training Instabilities via Dual Objectives](https://mlsanity.com/paper/2302.14320/) (2023)
- [Multi-Granularity Framework for Unsupervised Representation Learning of Time Series](https://mlsanity.com/paper/2312.07248/) (2023)
- [Smoothly Giving up: Robustness for Simple Models](https://mlsanity.com/paper/2302.09114/) (2023)
- [α-GAN by R'enyi Cross Entropy](https://mlsanity.com/paper/2505.14190/) (2025)

## Abstract (arXiv)

We present α-loss, α ∈ [1,∞], a tunable loss function for binary classification that bridges log-loss (α=1) and 0-1 loss (α = ∞). We prove that α-loss has an equivalent margin-based form and is classification-calibrated, two desirable properties for a good surrogate loss function for the ideal yet intractable 0-1 loss. For logistic regression-based classification, we provide an upper bound on the difference between the empirical and expected risk at the empirical risk minimizers for α-loss by exploiting its Lipschitzianity along with recent results on the landscape features of empirical risk functions. Finally, we show that α-loss with α = 2 performs better than log-loss on MNIST for logistic regression.