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.

翻译：求解大规模多阶段随机规划（MSP）问题面临严峻挑战，因为常用的阶段式分解算法（包括随机对偶动态规划（SDDP））随着子问题规模及数量的增长，计算时间呈递增趋势。传统方法通过逐步累加阶段性子问题原始解和对偶解的子梯度切割平面，将值函数近似为分段线性凸函数。针对这些局限性，我们提出TranSDDP——一种基于Transformer的新型阶段式分解算法。该创新方法利用Transformer模型的结构优势，采用顺序方法整合子梯度切割平面以近似值函数。通过数值实验，我们验证了TranSDDP在求解MSP问题中的有效性：它能够高效生成值函数的分段线性近似，在保持解质量的同时显著缩短计算时间，从而为大规模多阶段随机规划问题的处理开辟了有前景的新途径。