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

arXiv: https://arxiv.org/abs/2105.01853 · HTML: https://mlsanity.com/paper/2105.01853/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 43 references that are in the map.
- First posted on arXiv 5 May 2021.

## Builds on (most cited first, 8 of 8)

- [Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management](https://mlsanity.com/paper/1705.09412/) (2017)
- [Iterative Algorithm Induced Deep-Unfolding Neural Networks: Precoding Design for Multiuser MIMO Systems](https://mlsanity.com/paper/2006.08099/) (2020)
- [Spatial Deep Learning for Wireless Scheduling](https://mlsanity.com/paper/1808.01486/) (2018)
- [Real-time Power System State Estimation and Forecasting via Deep Neural Networks](https://mlsanity.com/paper/1811.06146/) (2018)
- [Stochastic Majorization-Minimization Algorithms for Large-Scale Optimization](https://mlsanity.com/paper/1306.4650/) (2013)
- [Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems](https://mlsanity.com/paper/1406.5429/) (2014)
- [Deep Learning for Distributed Optimization: Applications to Wireless Resource Management](https://mlsanity.com/paper/1905.13378/) (2019)
- [Decomposition by Partial Linearization: Parallel Optimization of Multi-Agent Systems](https://mlsanity.com/paper/1302.0756/) (2013)

## Built on by (most cited first, 4 of 4)

- [Machine Learning for Large-Scale Optimization in 6G Wireless Networks](https://mlsanity.com/paper/2301.03377/) (2023)
- [A Single-Loop Deep Actor-Critic Algorithm for Constrained Reinforcement Learning with Provable Convergence](https://mlsanity.com/paper/2306.06402/) (2023)
- [Context-aware Constrained Reinforcement Learning Based Energy-Efficient Power Scheduling for Non-stationary XR Data Traffic](https://mlsanity.com/paper/2503.09391/) (2025)
- [Two-Timescale Joint Transmit and Pinching Beamforming for Pinching-Antenna Systems](https://mlsanity.com/paper/2504.16099/) (2025)

## Abstract (arXiv)

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.