Multistage Stochastic Decomposition: A Bridge between Stochastic Programming and Approximate Dynamic Programming

Suvrajeet Sen; Zhihong Zhou

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SPEPS Preprint

Author(s):	Suvrajeet Sen, Ohio State University Zhihong Zhou, University of Arizona
Title:	Multistage Stochastic Decomposition: A Bridge between Stochastic Programming and Approximate Dynamic Programming
Date of Acceptance:	19.03.2012
Submission Date:	13.03.2012
Series Title:	Stochastic Programming E-Print Series (SPEPS)
Editors:	Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint:	pdf (urn:nbn:de:kobv:11-100200569)
Keywords (eng):	multi-stage stochastic programming, sequential sampling, stochastic decomposition, approximate dynamic programming
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Abstract (eng):

Multi-stage stochastic programs (MSP) pose some of the more challenging optimization problems. Because such models can become rather intractable in general, it is important to design algorithms that can provide approximations which, in the long run, yield solutions that are arbitrarily close to an optimum. In this paper, we propose a statistically motivated sequential sampling method that is applicable to multi-stage stochastic linear programs, and we refer to it as the multistage stochastic decomposition (MSD) algorithm. As with earlier SD methods for two- stage stochastic linear programs, this approach preserves one of the most attractive features of SD: asymptotic convergence of the solutions can be proven (with probability one) without any iteration requiring more than a small sample-size. This data-driven approach also allows us to sequentially update value function approximations, and the computations themselves can be organized in a manner that decomposes the scenario generation (stochastic) process from the optimization computations. As a by-product of this study, we also show that SD algorithms are essentially approximate dynamic programming algorithms for SP. Our asymptotic analysis also reveals conceptual connections between multiple SP algorithms.

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