SDDP-Transformer: applying the transformer to generation of piecewise linear value function

Abstract

Stochastic dual dynamic programming (SDDP), the conventional stage-wise decomposition algorithm for large-scale multistage stochastic programs, approximates the value function by adding a supporting hyperplane at each iteration. In other words, SDDP is an algorithm that sequentially generates supporting hyperplane until converging to the solution. SDDP is known as a state-of-the-art method for solving multi-stage stochastic optimization problem, but it has a critical problem related to growing time complexity occurred by increasing size of subproblem as the algorithm progresses. Transformer is a sequence model that shows the best performance with an encoder-decoder structure based on attention mechanism. We propose a model that sequentially generates supporting hyperplanes to build piecewise linear lower bound for value function based on the structure of Transformer. Our model can decrease problem solving cost of SDDP without losing solution quality compared to original method across various multi-stage stochastic optimization problems.