Two-Stage Stochastic Optimization via Primal-Dual Decomposition and Deep Unrolling

• URL: http://arxiv.org/abs/2105.01853v1
• Date: Wed, 5 May 2021 03:36:00 GMT
• Title: Two-Stage Stochastic Optimization via Primal-Dual Decomposition and Deep Unrolling
• Authors: An Liu, Rui Yang, Tony Q. S. Quek and Min-Jian Zhao
• Abstract summary: Two-stage algorithmic optimization plays a critical role in various engineering and scientific applications. There still lack efficient algorithms, especially when the long-term and short-term variables are coupled in the constraints. We show that PDD-SSCA can achieve superior performance over existing solutions.
• Score: 86.85697555068168
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a two-stage stochastic optimization problem, in which a long-term optimization variable is coupled with a set of short-term optimization variables in both objective and constraint functions. Despite that two-stage stochastic optimization plays a critical role in various engineering and scientific applications, there still lack efficient algorithms, especially when the long-term and short-term variables are coupled in the constraints. To overcome the challenge caused by tightly coupled stochastic constraints, we first establish a two-stage primal-dual decomposition (PDD) method to decompose the two-stage problem into a long-term problem and a family of short-term subproblems. Then we propose a PDD-based stochastic successive convex approximation (PDD-SSCA) algorithmic framework to find KKT solutions for two-stage stochastic optimization problems. At each iteration, PDD-SSCA first runs a short-term sub-algorithm to find stationary points of the short-term subproblems associated with a mini-batch of the state samples. Then it constructs a convex surrogate for the long-term problem based on the deep unrolling of the short-term sub-algorithm and the back propagation method. Finally, the optimal solution of the convex surrogate problem is solved to generate the next iterate. We establish the almost sure convergence of PDD-SSCA and customize the algorithmic framework to solve two important application problems. Simulations show that PDD-SSCA can achieve superior performance over existing solutions.

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