Title: Data-Driven Distributionally Robust Optimization
In typical applications of stochastic optimization, the underlying distribution of the uncertain parameters is unknown and must be estimated from data. Unfortunately, small estimation errors often yield large errors and instability in the computed solutions. Distributionally Robust Optimization (DRO) is an increasingly popular paradigm for addressing these estimation errors and instability. The key to the approach is to form an ambiguity set of plausible distributions based on the data, and then compute a solution with best worst-case behavior across all distributions in this set.
In the first part of the talk, we propose a novel variant of data-driven DRO, termed Robust SAA, which combines sample average approximation and statistical hypothesis testing. In particular, we prove that Robust SAA is computationally tractable for a wide-class of problems, asymptotically optimal and enjoys a strong finite-sample performance guarantee. These theoretical guarantees translate into strong practical performance in a variety of applications. We present empirical comparisons of Robust SAA to SAA and other traditional DRO methods.
In the last part of the talk, we will explore the theoretical limits of this modeling methodology. Are the ambiguity sets underlying Robust SAA “best” possible, in some sense? By introducing a novel Bayesian framework, we show that the answer is “yes” for general optimization problems, but “no” when the optimization problem demonstrates additional structure, like convexity. In the finite-dimensional setting, we show how very simple modifications to Robust SAA can yield provably near-optimal sets.
Bio: Vishal Gupta an Assistant Professor in Data Sciences and Operations at the Marshall School of Business at USC. After completing his BA in Mathematics and Philosophy from Yale University, he completed Part III of the Mathematics Tripos at Cambridge University and then spent several years working at Barclays Capital in commodities modeling. He completed his PhD in Operations Research from MIT in 2014.
Vishal's research interests focus on using data to formulate new, tractable models for uncertainty and behavior in optimization. He is particularly interested in the interplay between estimation and optimization in applications from energy, risk management, consumer preferences and data-analytics.