# Normalized Online Learning

arXiv: https://arxiv.org/abs/1408.2065 · HTML: https://mlsanity.com/paper/1408.2065/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2014.

## Built on by (most cited first, 7 of 7)

- [Efficient First-Order Contextual Bandits: Prediction, Allocation, and Triangular Discrimination](https://mlsanity.com/paper/2107.02237/) (2021)
- [Scale-free Unconstrained Online Learning for Curved Losses](https://mlsanity.com/paper/2202.05630/) (2022)
- [Dynamic Regret for Strongly Adaptive Methods and Optimality of Online KRR](https://mlsanity.com/paper/2111.11550/) (2021)
- [Online Learning under Haphazard Input Conditions: A Comprehensive Review and Analysis](https://mlsanity.com/paper/2404.04903/) (2024)
- [Optimal Regret for Policy Optimization in Contextual Bandits](https://mlsanity.com/paper/2602.13700/) (2026)
- [Scale-free adaptive planning for deterministic dynamics & discounted rewards](https://mlsanity.com/paper/2604.18312/) (2026)
- [Comparing Normalization Methods for Portfolio Optimization with Reinforcement Learning](https://mlsanity.com/paper/2508.03910/) (2025)

## Abstract (arXiv)

We introduce online learning algorithms which are independent of feature scales, proving regret bounds dependent on the ratio of scales existent in the data rather than the absolute scale. This has several useful effects: there is no need to pre-normalize data, the test-time and test-space complexity are reduced, and the algorithms are more robust.