Uncertainty is traditionally modeled via probability distributions. However, observable statistical data can often be explained by many strikingly different distributions. This "uncertainty about the uncertainty" poses a major challenge for optimization problems with uncertain parameters: estimation errors in the parameters' distribution are amplified through the optimization process and lead to biased (overly optimistic) optimization results as well as post-decision disappointment in out-of-sample tests. The emerging field of distributionally robust optimization (DRO) seeks new optimization models whose solutions are optimized against all distributions consistent with the given prior information. Recent research results have shown that many DRO models can be solved in polynomial time even when the corresponding stochastic models are intractable. DRO models also offer a more realistic account of uncertainty and mitigate the post-decision disappointment characteristic of stochastic models. The course will provide an overview of the state-of-the art in DRO, focusing mainly on the theory distributionally linear and convex optimization, data-driven distributionally robust optimization, as well as applications in finance, statistics and machine learning.
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