Volumetric Spanners: An Efficient Exploration Basis for Learning
Abstract
Numerous machine learning problems require an exploration basis - a mechanism to explore the action space. We define a novel geometric notion of exploration basis with low variance, called volumetric spanners, and give efficient algorithms to construct such a basis. We show how efficient volumetric spanners give rise to the first efficient and optimal regret algorithm for bandit linear optimization over general convex sets. Previously such results were known only for specific convex sets, or under special conditions such as the existence of an efficient self-concordant barrier for the underlying set.
Cite
Text
Hazan et al. "Volumetric Spanners: An Efficient Exploration Basis for Learning." Annual Conference on Computational Learning Theory, 2014.Markdown
[Hazan et al. "Volumetric Spanners: An Efficient Exploration Basis for Learning." Annual Conference on Computational Learning Theory, 2014.](https://mlanthology.org/colt/2014/hazan2014colt-volumetric/)BibTeX
@inproceedings{hazan2014colt-volumetric,
title = {{Volumetric Spanners: An Efficient Exploration Basis for Learning}},
author = {Hazan, Elad and Karnin, Zohar Shay and Meka, Raghu},
booktitle = {Annual Conference on Computational Learning Theory},
year = {2014},
pages = {408-422},
url = {https://mlanthology.org/colt/2014/hazan2014colt-volumetric/}
}