Applied Mathematics Colloquium

Title: On the solution of optimization and variational problems in misspecified regimes

Abstract: We consider a class of optimization and variational problems that are misspecified in a parametric sense. Resolving this misspecification is assumed to require the solution of a distinct convex learning problem. Traditional sequential approaches that first solve the learning problem and then solve the correctly specified computational problem require that exact or accurate solutions are available in finite time. We consider an approach where both problems are solved simultaneously in optimization and variational regimes via standard first-order projected gradient, subgradient, and extra gradient methods. We provide global convergence results and rate analysis for the schemes where we quantify the degradation from learning. In the second part of the talk, we consider stochastic generalizations of the problem that require coupled stochastic approximation schemes. We will also mention related efforts to solve problems distributed stochastic optimization problems on time-varying graphs and misspecified MDPs.