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.

通过引入 TranSDDP，一种基于 Transformer 的分阶段分解算法，我们有效地为大规模多阶段随机规划问题生成了分段线性逼近，显著减少了计算时间同时保持解决方案的质量，从而标志着在处理大规模多阶段随机规划问题方面的一个有希望的进展。

基于 Transformer 的大规模多阶段随机优化的逐阶分解

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

The most common approaches for solving multistage stochastic programming
problems in the research literature have been to either use value functions
("dynamic programming") or scenario trees ("stochastic programming") to
approximate the impact of a decision now on the future. By contrast, common
industry practice is to use a deterministic approximation of the future which
is easier to understand and solve, but which is criticized for ignoring
uncertainty. We show that a parameterized version of a deterministic
optimization model can be an effective way of handling uncertainty without the
complexity of either stochastic programming or dynamic programming. We present
the idea of a parameterized deterministic optimization model, and in particular
a deterministic lookahead model, as a powerful strategy for many complex
stochastic decision problems. This approach can handle complex,
high-dimensional state variables, and avoids the usual approximations
associated with scenario trees or value function approximations. Instead, it
introduces the offline challenge of designing and tuning the parameterization.
We illustrate the idea by using a series of application settings, and
demonstrate its use in a nonstationary energy storage problem with rolling
forecasts.

本文介绍了一种参数化确定性优化模型的方法，以代替在解决多阶段随机规划问题时繁琐的随机或动态规划方法，该方法可以有效地处理不确定性，并用非定常储能问题和滚动预测演示了其应用。