Multidimensional Stochastic Approximation: Adaptive Algorithms and Applications

摘要

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.