Learning to Parameterize Recourse Models for Large-Scale Stochastic Optimization

In a hub-and-spokes architecture for parallel scenario-based decomposition of stochastic optimization problems, the information produced by a decomposition algorithm, such as Progressive Hedging (PH), is used to simultaneously solve related optimization problems and obtain upper and lower bounds. We propose a framework that integrates a parametric low-fidelity (LF) recourse model within this architecture. The LF parameterization is learned offline as a function of the first-stage decisions and scenarios using feedback from a high-fidelity (HF) recourse model to improve the quality of decisions when evaluated under the HF formulation. During optimization, the parameterized LF model is used in the hub to efficiently solve the scenario subproblems, while the HF recourse model is used in the spokes to recover feasible solutions and compute provable bounds on the optimal objective value. We implement the proposed framework in the mpi-sppy package and demonstrate its potential on a stochastic generation, transmission, and storage expansion planning problem, where the HF model uses a linear DC power-flow formulation, while the LF model uses a network-flow approximation.