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Gradient estimation for smooth stopping criteria

Part of: Classical measure theory Markov processes

Published online by Cambridge University Press:  15 June 2022

Bernd Heidergott Open the ORCID record for Bernd Heidergott [Opens in a new window]  and
Yijie Peng
Bernd Heidergott*
Affiliation:
Vrije Universiteit Amsterdam
Yijie Peng*
Affiliation:
Peking University
*
*Postal address: Department of Operations Analytics, De Boelelaan 1105, 1081 HV Amsterdam. Email address: b.f.heidergott@vu.nl
**Postal address: Guanhua School of Management, 52 Haidian Rd, Beijing. Email address: pengyijie@pku.edu.cn
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Abstract

We establish sufficient conditions for differentiability of the expected cost collected over a discrete-time Markov chain until it enters a given set. The parameter with respect to which differentiability is analysed may simultaneously affect the Markov chain and the set defining the stopping criterion. The general statements on differentiability lead to unbiased gradient estimators.

Keywords

Sensitivity analysisMonte Carlo simulationgradient estimation

MSC classification

Primary: 28A15: Abstract differentiation theory, differentiation of set functions
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Type
Original Article
Information
Advances in Applied Probability , Volume 55 , Issue 1 , March 2023 , pp. 29 - 55
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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