# On the alpha-loss Landscape in the Logistic Model

arXiv: https://arxiv.org/abs/2006.12406 · HTML: https://mlsanity.com/paper/2006.12406/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2020.

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

- [Realizing GANs via a Tunable Loss Function](https://mlsanity.com/paper/2106.05232/) (2021)
- [Smoothly Giving up: Robustness for Simple Models](https://mlsanity.com/paper/2302.09114/) (2023)
- [Minimax Generalized Cross-Entropy](https://mlsanity.com/paper/2603.19874/) (2026)

## Abstract (arXiv)

We analyze the optimization landscape of a recently introduced tunable class of loss functions called α-loss, α ∈ (0,∞], in the logistic model. This family encapsulates the exponential loss (α = 1/2), the log-loss (α = 1), and the 0-1 loss (α = ∞) and contains compelling properties that enable the practitioner to discern among a host of operating conditions relevant to emerging learning methods. Specifically, we study the evolution of the optimization landscape of α-loss with respect to α using tools drawn from the study of strictly-locally-quasi-convex functions in addition to geometric techniques. We interpret these results in terms of optimization complexity via normalized gradient descent.