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Distributionally Robust Stochastic and Online Optimization

Banff International Research Station for Mathematical Innovation and Discovery

We present decision/optimization models/problems driven by uncertain and online data, and show how analytical models and computational algorithms can be used to achieve solution efficiency and near optimality. First, we describe recent applications of the Distributionally Robust Optimization in medical decision making. Secondly,we consider a common practice of estimating only marginal distributions and substituting joint distribution by independent (product) distribution in stochastic optimization, where we study possible loss incurred on ignoring correlations and quantify that loss as Price of Correlations (POC). Thirdly, we describe an online combinatorial auction problem using online linear programming technologies. We discuss near-optimal algorithms for solving this surprisingly general class of distribution-free online problems under the assumption of random order of arrivals and some conditions on the data and size of the problem.

Mathematics; Operations research, mathematical programming; Probability theory and stochastic processes; Operation research

video/mp4

Author affiliation: Stanford University

2019-03-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69026

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/