Optimal Algorithms for Range Searching over Multi-Armed Bandits

Barman, S and Krishnamurthy, R and Rahul, S (2021) Optimal Algorithms for Range Searching over Multi-Armed Bandits. In: 30th International Joint Conference on Artificial Intelligence, IJCAI 2021, 19-27 Aug 2021, Virtual, Online, pp. 2177-2183.

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Abstract

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. © 2021 International Joint Conferences on Artificial Intelligence. All rights reserved.

Item Type:	Conference Paper
Publication:	IJCAI International Joint Conference on Artificial Intelligence
Publisher:	International Joint Conferences on Artificial Intelligence
Additional Information:	The copyright for this article belongs to International Joint Conferences on Artificial Intelligence
Keywords:	Artificial intelligence, 'current; Hitting sets; Multiarmed bandits (MABs); Optimal algorithm; Problem objective; Range searching; Real intervals; Real line; Sample complexity; Stochastics, Stochastic systems
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	18 Mar 2022 11:59
Last Modified:	18 Mar 2022 11:59
URI:	http://eprints.iisc.ac.in/id/eprint/71605

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