Computer Science > Machine Learning
[Submitted on 4 May 2021]
Title:Optimal Algorithms for Range Searching over Multi-Armed Bandits
View PDFAbstract:This paper studies a multi-armed bandit (MAB) version of the range-searching problem. In its basic form, range searching considers as input a set of points (on the real line) and a collection of (real) intervals. Here, with each specified point, we have an associated weight, and the problem objective is to find a maximum-weight point within every given interval.
The current work addresses range searching with stochastic weights: each point corresponds to an arm (that admits sample access) and the point's weight is the (unknown) mean of the underlying distribution. In this MAB setup, we develop sample-efficient algorithms that find, with high probability, near-optimal arms within the given intervals, i.e., we obtain PAC (probably approximately correct) guarantees. We also provide an algorithm for a generalization wherein the weight of each point is a multi-dimensional vector. The sample complexities of our algorithms depend, in particular, on the size of the optimal hitting set of the given intervals.
Finally, we establish lower bounds proving that the obtained sample complexities are essentially tight. Our results highlight the significance of geometric constructs -- specifically, hitting sets -- in our MAB setting.
References & Citations
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
Connected Papers (What is Connected Papers?)
CORE Recommender (What is CORE?)
IArxiv Recommender
(What is IArxiv?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.