Transformer-based Stagewise Decomposition for Large-Scale Multistage Stochastic Optimization
This work addresses efficiency issues in optimization for researchers and practitioners dealing with large-scale stochastic problems, representing an incremental improvement over existing decomposition methods.
The paper tackles the challenge of solving large-scale multistage stochastic programming problems, where traditional methods like SDDP have high time complexity, by introducing TranSDDP, a Transformer-based algorithm that reduces computation time while maintaining solution quality.
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.