From Data to Decisions: Multi-Stage Optimization under Uncertainty

In real world problems, we often have parameters that are not exactly known due to measurement, implementation, prediction errors, and uncertainty. When solving optimization problems, we want to find a solution that will be feasible and work well in practice despite these uncertainties. Finding such a solution becomes harder when dealing with a multi-stage problem, in which we need to devise a strategy to make the best decision at each stage, without knowing the future realization of the uncertainty. These problems arise in real-world applications such as inventory control, energy systems, portfolio management and many others.

In this talk, we will review existing robust and adaptive optimization approaches for solving two-stage and multi-stage optimization problems with uncertain parameters. Specifically, we look at the case of multi-stage linear stochastic optimization problems where the only information given about the underlying distribution is in the form of data. We suggest a model called sample robust-optimization (SRO) in which we robustify the decisions against perturbation in the data points. We show that SRO results in both asymptotic performance guarantees and a desirable structure amiable to approximation. We demonstrate the performance of such approximation in numerical experiments.