# Tighter bounds lead to improved classifiers

arXiv: https://arxiv.org/abs/1606.09202 · HTML: https://mlsanity.com/paper/1606.09202/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2016.

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

- [Tapered Off-Policy REINFORCE: Stable and efficient reinforcement learning for LLMs](https://mlsanity.com/paper/2503.14286/) (2025)
- [Supervised Fine Tuning on Curated Data is Reinforcement Learning (and can be improved)](https://mlsanity.com/paper/2507.12856/) (2025)
- [Adversarial Training Should Be Cast as a Non-Zero-Sum Game](https://mlsanity.com/paper/2306.11035/) (2023)

## Abstract (arXiv)

The standard approach to supervised classification involves the minimization of a log-loss as an upper bound to the classification error. While this is a tight bound early on in the optimization, it overemphasizes the influence of incorrectly classified examples far from the decision boundary. Updating the upper bound during the optimization leads to improved classification rates while transforming the learning into a sequence of minimization problems. In addition, in the context where the classifier is part of a larger system, this modification makes it possible to link the performance of the classifier to that of the whole system, allowing the seamless introduction of external constraints.