Transformer-based Stagewise Decomposition for Large-Scale Multistage Stochastic Optimization

TL;DR

This paper introduces TranSDDP, a Transformer-based algorithm that improves large-scale multistage stochastic programming by efficiently approximating value functions, reducing computation time while maintaining solution quality.

Contribution

It presents a novel Transformer-based approach for stagewise decomposition, enhancing efficiency in solving large-scale MSP problems compared to traditional methods.

Findings

TranSDDP significantly reduces computation time.

It maintains high solution quality.

Effective in large-scale MSP problems.

Abstract

Solving large-scale multistage stochastic programming (MSP) problems poses a significant challenge as commonly used stagewise decomposition algorithms, including stochastic dual dynamic programming (SDDP), face growing time complexity as the subproblem size and problem count increase. Traditional approaches approximate the value functions as piecewise linear convex functions by incrementally accumulating subgradient cutting planes from the primal and dual solutions of stagewise subproblems. Recognizing these limitations, we introduce TranSDDP, a novel Transformer-based stagewise decomposition algorithm. This innovative approach leverages the structural advantages of the Transformer model, implementing a sequential method for integrating subgradient cutting planes to approximate the value function. Through our numerical experiments, we affirm TranSDDP's effectiveness in addressing MSP problems. It efficiently generates a piecewise linear approximation for the value function, significantly reducing computation time while preserving solution quality, thus marking a promising progression in the treatment of large-scale multistage stochastic programming problems.