Adaptive sampling strategies for risk-averse stochastic optimization with constraints

We introduce adaptive sampling methods for risk-neutral and risk-averse stochastic programs with deterministic constraints. In particular, we propose a variant of the stochastic projected gradient method where the sample size used to approximate the reduced gradient is determined a posteriori and updated adaptively. We also propose an SQP-type method based on similar adaptive sampling principles. Both methods lead to a significant reduction in cost. Numerical experiments from finance and engineering illustrate the performance and efficacy of the presented algorithms. The methods here are applicable to a broad class of expectation-based risk measures, however, we focus mainly on expected risk and conditional value-at-risk minimization problems