# Mathematics Colloquium

#### Performance Bounds and Optimization of Stochastic Systems under Model Uncertainty

**Speaker:**
Paul Dupuis, Brown University

**Location:**
Warren Weaver Hall 1302

**Date:**
~~Monday, March 25, 2019, 3:45 p.m.~~ CANCELLED

**Synopsis:**

We consider the problem of characterizing system performance and optimization and control when there are parts of the model that cannot or will not be precisely identified. Specifically, we formulate the general problem as quantifying errors that result when a probabilistic “nominal” model P (which we consider as the design model, or the computational model), is used in place of the “true” model Q. The focus is on how these problems may be addressed using information divergences between Q and P, and in particular how variational formulas may be used to obtain bounds for the difference between performance measures under Q (the true) and under P (the design) in terms of the divergence. The most natural example of such a variational formula is that which links exponential integrals, ordinary integrals, and relative entropy (or Kullback-Leibler divergence). We review some useful properties of this duality, and discuss how it can be used to study sensitivity bounds, optimization under model uncertainty, and related issues. We also recall its relation to H-infinity control, a well-known deterministic method for handling model form uncertainty. The last part of the talk will focus on limitations of the use of relative entropy in this context and describe alternative divergences that can be used to (possibly) overcome some of these limitations.