Stochastic Dynamic Linear Programming: A Sequential Sampling Algorithm for Multistage Stochastic Linear Programming

Multistage stochastic programming deals with operational and planning problems that involve a sequence of decisions over time while responding to an uncertain future. Algorithms designed address multistage linear (MSLP) often rely upon scenario trees represent the underlying process. When this process exhibits stagewise independence, sampling-based techniques, particularly dual dynamic algorithm, have received wide acceptance. However, these methods still operate deterministic representation problem which uses so-called sample average approximation. In work, we present sequential sampling approach for MSLP allows decision assimilate newly sampled data recursively. We refer method as (SDLP) algorithm. Since use sampling, algorithm does not necessitate priori uncertainty, through either tree or approximation, both require knowledge/estimation distribution. This constitutes generalization decomposition two-stage models. The approximations used within SDLP may be viewed lens proximal via regularization. Furthermore, introduce notion basic feasible policies provide piecewise affine solution discovery scheme, is embedded optimization identify incumbent solutions in context iterations. Finally, show provides corresponding value function estimates along state trajectories asymptotically converge their optimal counterparts, probability one.