The open source mpi-sppy library is a Python package that is focused on providing scalable decomposition implementations of progressive hedging (PH) and related algorithms for general stochastic programs. Originally built on the Pyomo algebraic modeling language (AML), mpi-sppy has been used to solve million-scenario problem instances on HPC platforms, and emphasizes (but is not limited to) multi-stage mixed-integer models. In this talk, we provide an overview of recent capability developments in mpi-sppy, including (1) automatic computation of the PH penalty parameter, (2) warm-starting of PH solves based on solutions to previously solved instances, (3) alternative linearizations of the PH quadratic penalty objective terms, (4) advanced variable bounds-tightening methods, and (5) AML-independent extensions to mpi-sppy (allowing, e.g., AMPL or GAMS base models).

Stochastic gradient descent (SGD) or stochastic approximation has been widely used in model training and stochastic optimization. While there is a huge literature on analyzing its convergence, inference on the obtained solutions from SGD has only been recently studied, yet it is important due to the growing need for uncertainty quantification. We investigate two computationally cheap resampling-based methods to construct confidence intervals for SGD solutions. One uses multiple, but few, SGDs in parallel via resampling with replacement from the data, and another operates this in an online fashion. Our methods can be regarded as enhancements of established bootstrap schemes to substantially reduce the computation effort in terms of resampling requirements while bypassing the intricate mixing conditions in existing batching methods. We achieve these via a recent so-called cheap bootstrap idea and Berry-Esseen-type bound for SGD.

Planning for the future of the power grid is of growing importance due to a variety of concerns: increasing demand for electric power, a shift toward weather-dependent sources of power generation, and increasing uncertainty due to climate risks. In this setting of high variability and uncertainty, multi-stage stochastic capacity expansion planning (CEP) can be used to inform long-term transmission, generation, and storage investment in a power system. While various stochastic CEP models exist that can co-optimize investments in a network under uncertainty, many of these models take a simplified version of the power network, ignoring related power flow (PF) and unit commitment (UC) constraints, under the assumption that these short-term constraints are unimportant for long-term planning. In this talk, we present a two-stage CEP model that can include more realistic PF and UC constraints. Using the open-source Electrical Grid Research and Engineering Tools (EGRET) library, we show how EGRET's modular suite of power system tools, including PF and UC models, can be leveraged in a two-stage stochastic CEP model that is then solved via Progressive Hedging, and we discuss extensions to a multi-stage setting. Finally, we demonstrate the performance of our CEP model formulations on a large-scale synthetic-but-realistic California test case with over 8,000 buses and up to a year of representative future days. By comparing CEP results with and without UC and PF representations, we discuss how the solution changes when we consider these additional constraints.