Paper Info
Title
Dynamic Stochastic Approximation For Multi-Stage Stochastic Optimization
Abstract
In this paper, we consider multi-stage stochastic optimization problems with convex objectives and conic constraints at each stage. We present a new stochastic first-order method, namely the dynamic stochastic approximation (DSA) algorithm, for solving these types of stochastic optimization problems. We show that DSA can achieve an optimal O(1/epsilon 4) rate of convergence in terms of the total number of required scenarios when applied to a three-stage stochastic optimization problem. We further show that this rate of convergence can be improved to O(1/epsilon 2) when the objective function is strongly convex. We also discuss variants of DSA for solving more general multi-stage stochastic optimization problems with the number of stages T>3. The developed DSA algorithms only need to go through the scenario tree once in order to compute an epsilon-solution of the multi-stage stochastic optimization problem. As a result, the memory required by DSA only grows linearly with respect to the number of stages. To the best of our knowledge, this is the first time that stochastic approximation type methods are generalized for multi-stage stochastic optimization with T >= 3.
Year
DOI
Venue
2017
10.1007/s10107-020-01489-y
MATHEMATICAL PROGRAMMING
Field
DocType
Volume
Mathematical optimization,Stochastic optimization,Discrete-time stochastic process,Stochastic calculus,Continuous-time stochastic process,Stochastic partial differential equation,Stochastic programming,Stochastic approximation,Mathematics,Stochastic control
Journal
187
Issue
ISSN
Citations 
1-2
0025-5610
0
PageRank 
References 
Authors
0.34
16
2
Name
Order
Citations
PageRank
Guanghui Lan1121266.26
Zhiqiang Zhou27911.05