Robust sample average approximation with small sample sizes

We consider solving stochastic optimization problems in which we seek to minimize the expected value of an objective function with respect to an unknown distribution of random parameters. Our focus is on models that use sample average approximation (SAA) with small sample sizes. We analyse the out-of-sample performance of solutions obtained by solving a robust version of the SAA problem, and derive conditions under which these solutions are improved in comparison with SAA. We analyse three different mechanisms for constructing a robust solution: a CVaR-based risk measure, phi-divergence using total variation, and a Wasserstein metric.