Projective Hedging Algorithms for Multistage Stochastic Programming, Supporting Distributed and Asynchronous Implementation

In “Projective Hedging Algorithms for Multistage Stochastic Programming, Supporting Distributed and Asynchronous Implementation,” Eckstein, Watson, and Woodruff derive a new class of decomposition methods for convex multistage stochastic programs defined on finite but potentially large scenario trees. These methods resemble Rockafellar and Wets’ now-classical progressive hedging (PH) method but are based on a flexible projective operator-splitting scheme instead of the standard alternating direction method of multipliers (ADMM). The new algorithms only need to reoptimize subproblems for a subset of the scenarios at each iteration, instead of all of them, and are also amenable to a form of asynchronous implementation, without the algorithm randomization or small step-size requirements usually imposed in such contexts. In the online appendix, the authors demonstrate significant computational gains over PH, applying hundreds or thousands of processor cores to problem instances with up to a million scenarios.