We present decision/optimization models/problems driven by uncertain and online data, and show how analytical models and computational algorithms can be used to improve decision and learning quality.
- First, we describe the so-called Distributionally or Likelihood Robust optimization (DRO) models and their algorithms in dealing stochastic decision problems when the exact uncertainty distribution is unknown but certain statistical moments and/or sample distributions are known.
- Secondly, when decisions are made in presence of high dimensional stochastic data, handling joint distribution of correlated random variables can present a formidable task. A common heuristic is to estimate only marginal distributions and substitute joint distribution by independent (product) distribution. Here, we study possible loss incurred on ignoring correlations through the DRO approach, and quantify that loss as Price of Correlations (POC).
- Thirdly, we describe an online combinatorial auction problem using online linear programming technologies. We discuss several near-optimal algorithms for solving this surprisingly general class of online problems under the assumption of random order of arrivals and some conditions on the data and size of the problem.
