Acceleration of stochastic approximation by averaging
SIAM Journal on Control and Optimization
A scaled stochastic approximation algorithm
Management Science
A projected stochastic approximation algorithm
WSC '91 Proceedings of the 23rd conference on Winter simulation
Global Stochastic Optimization with Low-Dispersion Point Sets
Operations Research
Introduction to Stochastic Search and Optimization
Introduction to Stochastic Search and Optimization
Simulation Modeling and Analysis with Expertfit Software
Simulation Modeling and Analysis with Expertfit Software
Retrospective-approximation algorithms for the multidimensional stochastic root-finding problem
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Markov Chains and Stochastic Stability
Markov Chains and Stochastic Stability
The stochastic root-finding problem: Overview, solutions, and open questions
ACM Transactions on Modeling and Computer Simulation (TOMACS)
An adaptive multidimensional version of the Kiefer-Wolfowitz stochastic approximation algorithm
Winter Simulation Conference
Averaging and derivative estimation within stochastic approximation algorithms
Proceedings of the Winter Simulation Conference
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Consider multi-dimensional root finding when the equations are available only implicitly via a Monte Carlo simulation oracle that for any solution returns a vector of point estimates. We develop DARTS, a stochastic-approximation algorithm that makes quasi-Newton moves to a new solution whenever the current sample size is large compared to the estimated quality of the current solution and estimated sampling error. We show that DARTS converges in a certain precise sense, and discuss reasons to expect substantial computational efficiencies over traditional stochastic approximation variations.