Scaling Up the Sample Average Approximation Method for Stochastic Optimization with Applications to Trading Agents

Amy Greenwald, Bryan Guillemette, Victor Naroditskiy, Michael Carl Tschantz

Abstract: The Sample Average Approximation (SAA) method is a technique for approximating solutions to stochastic programs. Here, we attempt to scale up the SAA method to harder problems than those previously studied. We argue that to apply the SAA method effectively, there are three parameters to optimize: the number of evaluations, the number of scenarios, and the number of candidate solutions. We propose an experimental methodology for finding the optimal settings of these parameters given fixed time and space constraints. We apply our methodology to two large-scale stochastic optimization problems that arise in the context of the annual Trading Agent Competition. Both problems are expressed as integer linear programs and solved using CPLEX. Runtime increases linearly with the number of scenarios in one of the problems, and exponentially in the other. We find that, in the former problem, maximizing the number of scenarios yields the best solution, while in the latter problem, it is necessary to evaluate multiple candidate solutions to find the best solution, since increasing the number of scenarios becomes expensive very quickly.