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EXPLORATION–EXPLOITATION POLICIES WITH ALMOST SURE, ARBITRARILY SLOW GROWING ASYMPTOTIC REGRET

Part of: Nonparametric inference

Published online by Cambridge University Press:  26 January 2019

Wesley Cowan  and
Michael N. Katehakis
Wesley Cowan
Affiliation:
Department of Computer Science, Rutgers University, Piscataway, NJ08854, USA E-mail: cwcowan@math.rutgers.edu
Michael N. Katehakis
Affiliation:
Department of Management Science and Information Systems, Rutgers University, Piscataway, NJ08854, USA E-mail: mnk@rutgers.edu
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Abstract

The purpose of this paper is to provide further understanding into the structure of the sequential allocation (“stochastic multi-armed bandit”) problem by establishing probability one finite horizon bounds and convergence rates for the sample regret associated with two simple classes of allocation policies. For any slowly increasing function g, subject to mild regularity constraints, we construct two policies (the g-Forcing, and the g-Inflated Sample Mean) that achieve a measure of regret of order O(g(n)) almost surely as n → ∞, bound from above and below. Additionally, almost sure upper and lower bounds on the remainder term are established. In the constructions herein, the function g effectively controls the “exploration” of the classical “exploration/exploitation” tradeoff.

Keywords

banditsforcing actionsinflated sample meansmulti-armedonline learningsequential allocationupper confidence bounds

MSC classification

Primary: 62G05: Estimation
Secondary: 62G20: Asymptotic properties
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Special Issue 3: Analytic Methods in Health Care and in Clinical Trials In Honor and Memory of Lycourgos (Lee) Papayanopoulos , July 2020 , pp. 406 - 428
Copyright
Copyright © Cambridge University Press 2019

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