# Regularized Decomposition of High-Dimensional Multistage Stochastic Programs with Markov Uncertainty

arXiv: https://arxiv.org/abs/1505.02227 · HTML: https://mlsanity.com/paper/1505.02227/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2015.

## Built on by (most cited first, 1 of 1)

- [Learning Optimal Power Flow Value Functions with Input-Convex Neural Networks](https://mlsanity.com/paper/2310.04605/) (2023)

## Abstract (arXiv)

We develop a quadratic regularization approach for the solution of high-dimensional multistage stochastic optimization problems characterized by a potentially large number of time periods/stages (e.g. hundreds), a high-dimensional resource state variable, and a Markov information process. The resulting algorithms are shown to converge to an optimal policy after a finite number of iterations under mild technical assumptions. Computational experiments are conducted using the setting of optimizing energy storage over a large transmission grid, which motivates both the spatial and temporal dimensions of our problem. Our numerical results indicate that the proposed methods exhibit significantly faster convergence than their classical counterparts, with greater gains observed for higher-dimensional problems.