Multi-Armed Bandits with Bounded Arm-Memory: Near-Optimal Guarantees for Best-Arm Identification and Regret Minimization

Maiti, A and Patil, V and Khan, A (2021) Multi-Armed Bandits with Bounded Arm-Memory: Near-Optimal Guarantees for Best-Arm Identification and Regret Minimization. In: 35th Conference on Neural Information Processing Systems, NeurIPS 2021, 6 December 2021 through 14 December 2021, Virtual, Online, pp. 19553-19565.

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Abstract

Abstract We study the Stochastic Multi-armed Bandit problem under bounded arm-memory. In this setting, the arms arrive in a stream, and the number of arms that can be stored in the memory at any time, is bounded. The decision-maker can only pull arms that are present in the memory. We address the problem from the perspective of two standard objectives: 1) regret minimization, and 2) best-arm identification. For regret minimization, we settle an important open question by showing an almost tight guarantee. We show Q(T2/3) cumulative regret in expectation for single-pass algorithms for arm-memory size of (n - 1), where n is the number of arms. For best-arm identification, we provide an (e, <5)-PAC algorithm with arm-memory size of 0(log∗ n) and • log^)) optimal sample complexity.

Item Type:	Conference Paper
Publication:	Advances in Neural Information Processing Systems
Publisher:	Neural information processing systems foundation
Additional Information:	The copyright for this article belongs to the Neural information processing systems foundation.
Keywords:	ARM processors; Decision making, Decision makers; Memory size; Multiarmed bandit problems (MABP); Multiarmed bandits (MABs); Near-optimal; Number of arms; Optimal samples; Regret minimization; Single-pass algorithm; Stochastics, Stochastic systems
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	27 Jun 2022 07:26
Last Modified:	27 Jun 2022 07:26
URI:	https://eprints.iisc.ac.in/id/eprint/73995

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