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

TL;DR

This paper introduces a quadratic regularization method for efficiently solving high-dimensional multistage stochastic programs with Markov uncertainty, demonstrating faster convergence in energy storage optimization scenarios.

Contribution

The paper presents a novel quadratic regularization approach tailored for high-dimensional multistage stochastic problems with Markov processes, ensuring finite convergence and improved computational performance.

Findings

Faster convergence compared to classical methods

Significant improvements in high-dimensional settings

Effective in energy storage optimization over large grids

Abstract

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.