  The progressive hedging algorithm (PHA) is a cornerstone among algorithms for
large-scale stochastic programming problems. However, its traditional
implementation is hindered by some limitations, including the requirement to
solve all scenario subproblems in each iteration, reliance on an explicit
probability distribution, and a convergence process that is highly sensitive to
the choice of certain penalty parameters. This paper introduces a
sampling-based PHA which aims to overcome these limitations. Our approach
employs a dynamic selection process for the number of scenario subproblems
solved per iteration. It incorporates adaptive sequential sampling for
determining sample sizes, a stochastic conjugate subgradient method for
direction finding, and a line-search technique to update the dual variables.
Experimental results demonstrate that this novel algorithm not only addresses
the bottlenecks of the conventional PHA but also potentially surpasses its
scalability, representing a substantial improvement in the field of stochastic
programming.
