Randomized Progressive Hedging methods for Multi-stage Stochastic Programming

TL;DR

This paper introduces randomized variants of the Progressive Hedging algorithm for multi-stage stochastic programming, enabling faster solutions by solving only one scenario subproblem per iteration and leveraging recent fixed point methods.

Contribution

It proposes novel randomized algorithms for Progressive Hedging, analyzes their convergence, and provides a Julia toolbox, improving computational efficiency especially in parallel settings.

Findings

Randomized algorithms reduce computational time.

Parallel implementation enhances scalability.

Code availability facilitates adoption.

Abstract

Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this paper, we introduce randomized versions of the Progressive Hedging algorithm able to produce new iterates as soon as a single scenario subproblem is solved. Building on the relation between Progressive Hedging and monotone operators, we leverage recent results on randomized fixed point methods to derive and analyze the proposed methods. Finally, we release the corresponding code as an easy-to-use Julia toolbox and report computational experiments showing the practical interest of randomized algorithms, notably in a parallel context. Throughout the paper, we pay a special attention to presentation, stressing main ideas, avoiding extra-technicalities, in order to make the randomized methods accessible to a broad audience in the Operations Research community.