Two-Stage Stochastic Optimization Via Primal-Dual Decomposition and Deep Unrolling Article Swipe

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An Liu , Rui Yang , Tony Q. S. Quek , Minjian Zhao ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.1109/tsp.2021.3079807

We consider a two-stage stochastic optimization problem, in which a long-term\noptimization variable is coupled with a set of short-term optimization\nvariables in both objective and constraint functions. Despite that two-stage\nstochastic optimization plays a critical role in various engineering and\nscientific applications, there still lack efficient algorithms, especially when\nthe long-term and short-term variables are coupled in the constraints. To\novercome the challenge caused by tightly coupled stochastic constraints, we\nfirst establish a two-stage primal-dual decomposition (PDD) method to decompose\nthe two-stage problem into a long-term problem and a family of short-term\nsubproblems. Then we propose a PDD-based stochastic successive convex\napproximation (PDD-SSCA) algorithmic framework to find KKT solutions for\ntwo-stage stochastic optimization problems. At each iteration, PDD-SSCA first\nruns a short-term sub-algorithm to find stationary points of the short-term\nsubproblems associated with a mini-batch of the state samples. Then it\nconstructs a convex surrogate for the long-term problem based on the deep\nunrolling of the short-term sub-algorithm and the back propagation method.\nFinally, the optimal solution of the convex surrogate problem is solved to\ngenerate the next iterate. We establish the almost sure convergence of PDD-SSCA\nand customize the algorithmic framework to solve two important application\nproblems. Simulations show that PDD-SSCA can achieve superior performance over\nexisting solutions.\n

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Mathematical Analysis

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Mathematical optimization Karush–Kuhn–Tucker conditions Optimization problem Stochastic optimization Stochastic programming Term (time) Computer science Convex optimization Mathematics Convergence (economics) Stationary point Regular polygon Physics Economic growth Quantum mechanics Geometry Economics Mathematical analysis

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Type: article
Language: en
Landing Page: https://doi.org/10.1109/tsp.2021.3079807
OA Status: green
Cited By: 12
References: 44
Related Works: 10
OpenAlex ID: https://openalex.org/W3160297086

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DOI: https://doi.org/10.1109/tsp.2021.3079807

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Title: Two-Stage Stochastic Optimization Via Primal-Dual Decomposition and Deep Unrolling

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Language: en

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Publication year: 2021

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Publication date: 2021-01-01

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Authors: An Liu, Rui Yang, Tony Q. S. Quek, Minjian Zhao

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Landing page: https://doi.org/10.1109/tsp.2021.3079807

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Concepts: Mathematical optimization, Karush–Kuhn–Tucker conditions, Optimization problem, Stochastic optimization, Stochastic programming, Term (time), Computer science, Convex optimization, Mathematics, Convergence (economics), Stationary point, Regular polygon, Physics, Economic growth, Quantum mechanics, Geometry, Economics, Mathematical analysis

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Cited by: 12

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