A unified view of the IPA, SF, and LR gradient estimation techniques
Management Science
Acceleration of stochastic approximation by averaging
SIAM Journal on Control and Optimization
Cross-entropy and rare events for maximal cut and partition problems
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue: Rare event simulation
Budget-Dependent Convergence Rate of Stochastic Approximation
SIAM Journal on Optimization
Introduction to Stochastic Search and Optimization
Introduction to Stochastic Search and Optimization
The Cross Entropy Method: A Unified Approach To Combinatorial Optimization, Monte-carlo Simulation (Information Science and Statistics)
Approximate zero-variance simulation
Proceedings of the 40th Conference on Winter Simulation
Rare Event Simulation using Monte Carlo Methods
Rare Event Simulation using Monte Carlo Methods
Asymptotic robustness of estimators in rare-event simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
The stochastic root-finding problem: Overview, solutions, and open questions
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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We propose an adaptive parameterized method to approximate the zero-variance change of measure for the evaluation of static network reliability models, with links subject to failures. The method uses two rough approximations of the unreliability function, conditional on the states of any subset of links being fixed. One of these approximations, based on mincuts, under-estimates the true unknown unreliability, whereas the other one, based on minpaths, over-estimates it. Our proposed change of measure takes a convex linear combination of the two, estimates the optimal (graph-dependent) coefficient in this combination from pilot runs, and uses the resulting conditional unreliability approximation at each step of a dynamic importance sampling algorithm. This new scheme is more general and more flexible than a previously proposed zero-variance approximation scheme, based on mincuts only, and which was shown to be robust asymptotically when unreliabilities of individual links decrease toward zero. Our numerical examples show that the new scheme is often more efficient when low unreliability comes from a large number of possible paths connecting the considered nodes rather than from small failure probabilities of the links.