On sample size control in sample average approximations for solving smooth stochastic programs

We consider smooth stochastic programs and develop a discrete‐time optimal‐control problem for adaptively selecting sample sizes in a class of algorithms based on variable sample average approximations (VSAA). The control problem aims to minimize the expected computational cost to obtain a near‐optimal solution of a stochastic program and is solved approximately using dynamic programming. The optimal‐control problem depends on unknown parameters such as rate of convergence, computational cost per iteration, and sampling error. Hence, we implement the approach within a receding‐horizon framework where parameters are estimated and the optimal‐control problem is solved repeatedly during the calculations of a VSAA algorithm. The resulting sample‐size selection policy consistently produces near‐optimal solutions in short computing times as compared to other plausible policies in several numerical examples.