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Complete expected improvement converges to an optimal budget allocation

Part of: Artificial intelligence (68Txx) Stochastic systems and control

Published online by Cambridge University Press:  22 July 2019

Ye Chen  and
Ilya O. Ryzhov
Ye Chen*
Affiliation:
Virginia Common wealth University
Ilya O. Ryzhov*
Affiliation:
University of Maryland
*
*Postal address: Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284, USA.
**Postal address: Robert H. Smith School of Business, University of Maryland, College Park, MD 20742, USA. Email address: iryzhov@rhsmith.umd.edu
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Abstract

The ranking and selection problem is a well-known mathematical framework for the formal study of optimal information collection. Expected improvement (EI) is a leading algorithmic approach to this problem; the practical benefits of EI have repeatedly been demonstrated in the literature, especially in the widely studied setting of Gaussian sampling distributions. However, it was recently proved that some of the most well-known EI-type methods achieve suboptimal convergence rates. We investigate a recently proposed variant of EI (known as ‘complete EI’) and prove that, with some minor modifications, it can be made to converge to the rate-optimal static budget allocation without requiring any tuning.

Keywords

Optimal learningranking and selectionexpected improvementlarge deviations rate

MSC classification

Primary: 93E35: Stochastic learning and adaptive control
Secondary: 68T05: Learning and adaptive systems
Type
Original Article
Information
Advances in Applied Probability , Volume 51 , Issue 1 , March 2019 , pp. 209 - 235
Copyright
© Applied Probability Trust 2019 

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