# Generalized Translation and Scale Invariant Online Algorithm for Adversarial Multi-Armed Bandits

arXiv: https://arxiv.org/abs/2109.09212 · HTML: https://mlsanity.com/paper/2109.09212/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 72 references that are in the map.
- First posted on arXiv 19 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [Recursive Experts: An Efficient Optimal Mixture of Learning Systems in Dynamic Environments](https://mlsanity.com/paper/2009.09249/) (2020)
- [Minimax Optimal Algorithms for Adversarial Bandit Problem with Multiple Plays](https://mlsanity.com/paper/1911.11122/) (2019)
- [RELEAF: An Algorithm for Learning and Exploiting Relevance](https://mlsanity.com/paper/1502.01418/) (2015)
- [Distributed Online Learning in Social Recommender Systems](https://mlsanity.com/paper/1309.6707/) (2013)
- [A Comprehensive Approach to Universal Piecewise Nonlinear Regression Based on Trees](https://mlsanity.com/paper/1311.6392/) (2013)
- [Feedback Solution to Optimal Switching Problems with Switching Cost](https://mlsanity.com/paper/1411.4695/) (2014)

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

- [Second Order Regret Bounds Against Generalized Expert Sequences under Partial Bandit Feedback](https://mlsanity.com/paper/2204.06660/) (2022)
- [Data Dependent Regret Guarantees Against General Comparators for Full or Bandit Feedback](https://mlsanity.com/paper/2303.06526/) (2023)

## Abstract (arXiv)

We study the adversarial multi-armed bandit problem and create a completely online algorithmic framework that is invariant under arbitrary translations and scales of the arm losses. We study the expected performance of our algorithm against a generic competition class, which makes it applicable for a wide variety of problem scenarios. Our algorithm works from a universal prediction perspective and the performance measure used is the expected regret against arbitrary arm selection sequences, which is the difference between our losses and a competing loss sequence. The competition class can be designed to include fixed arm selections, switching bandits, contextual bandits, or any other competition of interest. The sequences in the competition class are generally determined by the specific application at hand and should be designed accordingly. Our algorithm neither uses nor needs any preliminary information about the loss sequences and is completely online. Its performance bounds are the second order bounds in terms of sum of the squared losses, where any affine transform of the losses has no effect on the normalized regret.