Neural Stochastic Dual Dynamic Programming

Multi-stage stochastic optimization (MSSO) considers the problem of optimizing a sequence of decisions over a finite number of stages in the presence of stochastic observations, minimizing an expected cost while ensuring stage-wise action constraints are satisfied (Birge and Louveaux, 2011; Shapiro et al., 2014). Such a problem formulation captures a diversity of real-world process optimization problems, such as asset allocation (Dantzig and Infanger, 1993), inventory control (Shapiro et al., 2014; Nambiar et al., 2021), energy planning (Pereira and Pinto, 1991), and bio-chemical process control (Bao et al., 2019), to name a few. Despite the importance and ubiquity of the problem, it has proved challenging to develop algorithms that can cope with high-dimensional action spaces and long-horizon problems (Shapiro and Nemirovski, 2005; Shapiro, 2006). There have been a number of attempts to design scalable algorithms for MSSO, which generally attempt to exploit scenarios-wise or stage-wise decompositions. An example of a scenario-wise approach is Rockafellar and Wets (1991), which proposed a progressive hedging algorithm that decomposes the sample averaged approximation of the problem into individual scenarios and applies an augmented Lagrangian method to achieve consistency in a final solution.