Zuvor findet um 16:45 Uhr die Teerunde in Raum 244 des Mathematikgebäudes (S2|15) Schlossgartenstr. 7, statt.
Prof. Dr. Christian Bender, Universität des Saarlandes
We consider the single-stage stochastic optimization problem to minimize the expected cost over a set of decisions. Motivated by the dual formulation of optimal stopping problems we focus on the following situation: The set of minimizers is infinite and there is at least one „surely optimal“ decision, i.e., a minimizer whose cost has zero variance. A classical method for solving stochastic optimization problems numerically is sample average approximation (SAA), a Monte Carlo method which replaces the expectation by the empirical mean over a simulated sample and then applies deterministic algorithms to search for a minimizer of the approximate problem. While SAA is known to converge to an optimal decision under appropriate assumptions, we illustrate that it may fail to converge to a surely optimal decision. In order to exploit the zero-variance property of surely optimal decisions we suggest a randomization of the original optimization problem, which enforces convergence of SAA to surely optimal decisions, while preserving the structure of the problem (e.g., convexity or linear programming formulation of the deterministic problem). We state improved convergence properties of the randomization approach in the framework of optimal stopping and illustrate the results in some numerical experiments.
25. Januar 2023, 17:00-19:00
Uhrturmhörsaal der Physik