Multidimensional stochastic approximation: Adaptive algorithms and applications

Authors:
Mark Broadie;Deniz M. Cicek;Assaf Zeevi
Affiliations:
Columbia University;Columbia University;Columbia University
Venue:
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on simulation in complex service systems
Year:
2014

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Abstract

We consider prototypical sequential stochastic optimization methods of Robbins-Monro (RM), Kiefer-Wolfowitz (KW), and Simultaneous Perturbations Stochastic Approximation (SPSA) varieties and propose adaptive modifications for multidimensional applications. These adaptive versions dynamically scale and shift the tuning sequences to better match the characteristics of the unknown underlying function, as well as the noise level. We test our algorithms on a variety of representative applications in inventory management, health care, revenue management, supply chain management, financial engineering, and queueing theory.