Analysis of an importance sampling estimator for tandem queues
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Fast simulation of rare events in queueing and reliability models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Efficient suboptimal rare-event simulation
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Approximate zero-variance simulation
Proceedings of the 40th Conference on Winter Simulation
Subsolutions of an Isaacs Equation and Efficient Schemes for Importance Sampling
Mathematics of Operations Research
Uniformly Efficient Importance Sampling for the Tail Distribution of Sums of Random Variables
Mathematics of Operations Research
Asymptotic robustness of estimators in rare-event simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Introduction to Rare Event Simulation
Introduction to Rare Event Simulation
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Importance sampling is widely perceived as an indispensable tool in Monte Carlo estimation for rare-event problems. It is also known, however, that constructing efficient importance sampling scheme requires in many cases a precise knowledge of the underlying stochastic structure. This paper considers the simplest problem in which part of the system is not directly known. Namely, we consider the tail probability of a monotone function of sum of independent and identically distributed (i.i.d.) random variables, where the function is only accessible through black-box simulation. A simple two-stage procedure is proposed whereby the function is learned in the first stage before importance sampling is applied. We discuss some sufficient conditions for the procedure to retain asymptotic optimality in well-defined sense, and discuss the optimal computational allocation. Simple analysis shows that the procedure is more beneficial than a single-stage mixture-based importance sampler when the computational cost of learning is relatively light.