NDLI: Combining importance sampling and temporal difference control variates to simulate Markov Chains

Content Provider	ACM Digital Library
Author	Randhawa, R. S. Juneja, S.
Copyright Year	2004
Abstract	It is well known that in estimating performance measures associated with a stochastic system a good importance sampling distribution (IS) can give orders of magnitude of variance reduction while a bad one may lead to large, even infinite, variance. In this paper we study how this sensitivity of the estimator variance to the importance sampling change of measure may be "dampened" by combining importance sampling with stochastic approximation based temporal difference (TD) method. We consider a finite state space discrete time Markov chain (DTMC) with one-step transition rewards and an absorbing set of states and focus on estimating the cumulative expected reward to absorption starting from any state. In this setting we develop sufficient conditions under which the estimate resulting from the combined approach has a mean square error that asymptotically equals zero even when the estimate formed by using only importance sampling change of measure has infinite variance. In particular, we consider the problem of estimating the small buffer overflow probability in a queuing network, where the change of measure suggested in literature is shown to have infinite variance under certain parameters and where the appropriate combination of IS and TD method can be empirically seen to have a much faster convergence rate compared to naive simulation.
Starting Page	1
Ending Page	30
Page Count	30
File Format	PDF
ISSN	10493301
e-ISSN	15581195
DOI	10.1145/974734.974735
Volume Number	14
Issue Number	1
Journal	ACM Transactions on Modeling and Computer Simulation (TOMACS)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2004-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Importance sampling Markov chains Rare events Stochastic approximation Temporal difference methods Variance reduction
Content Type	Text
Resource Type	Article
Subject	Computer Science Applications Modeling and Simulation

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