Stopping Rules for a Class of Sampling-Based Stochastic Programming Algorithms

Decomposition and Monte Carlo sampling-based algorithms hold much promise for solving stochastic programs with many scenarios. A critical component of such algorithms is a stopping criterion to ensure the quality of the solution. In this paper, we develop a stopping rule theory for a class of algorithms that estimate bounds on the optimal objective function value by sampling. We provide rules for selecting sample sizes and terminating the algorithm under which asymptotic validity of confidence intervals for the quality of the proposed solution can be verified. These rules are applied to a multistage stochastic linear programming algorithm due to Pereira and Pinto.