# Bandit Regret Scaling with the Effective Loss Range

arXiv: https://arxiv.org/abs/1705.05091 · HTML: https://mlsanity.com/paper/1705.05091/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2017.

## Built on by (most cited first, 2 of 2)

- [Scale Free Adversarial Multi Armed Bandits](https://mlsanity.com/paper/2106.04700/) (2021)
- [Nested bandits](https://mlsanity.com/paper/2206.09348/) (2022)

## Abstract (arXiv)

We study how the regret guarantees of nonstochastic multi-armed bandits can be improved, if the effective range of the losses in each round is small (e.g. the maximal difference between two losses in a given round). Despite a recent impossibility result, we show how this can be made possible under certain mild additional assumptions, such as availability of rough estimates of the losses, or advance knowledge of the loss of a single, possibly unspecified arm. Along the way, we develop a novel technique which might be of independent interest, to convert any multi-armed bandit algorithm with regret depending on the loss range, to an algorithm with regret depending only on the effective range, while avoiding predictably bad arms altogether.