Invited Session Thu.3.MA 141

Thursday, 15:15 - 16:45 h, Room: MA 141

Cluster 22: Stochastic optimization [...]

Measures of uncertainty


Chair: Marida Bertocchi



Thursday, 15:15 - 15:40 h, Room: MA 141, Talk 1

Francesca Maggioni
Measures of information in multistage stochastic programming

Coauthors: Elisabetta Allevi, Marida Bertocchi


Multistage stochastic programs, which involve sequences of decisions over time, are usually hard to solve in realistically sized problems. Providing bounds for their optimal solution, may help in evaluating whether it is worth the additional computations for the stochastic program versus simplified approaches. In this talk we generalize the value of information gained from deterministic, pair solutions and rolling-horizon approximation in the two-stage case to the multistage stochastic formulation. With respect to the former we introduce the Multistage Expected Value of the Reference Scenario, MEVRS, the Multistage Sum of Pairs Expected Values, MSPEV and the Multistage Expectation of Pairs Expected Value, MEPEV by means of the new concept of auxiliary scenario and redefinition of pairs subproblems probability. We show that theorems proved for two stage case are valid also in the multi-stage case. With respect to the latter, the rolling time horizon procedure allows to update the estimations of the solution at each stage. New measures of quality of the average solution are of practical relevance. Numerical results on a case study illustrate the relationships.



Thursday, 15:45 - 16:10 h, Room: MA 141, Talk 2

Simone Garatti
The risk of empirical costs in randomized min-max stochastic optimization

Coauthors: Marco C. Campi, Algo Carè


We consider convex min-max stochastic optimization. By sampling the uncertain parameter, the min-max solution that satisfies the sampled instances of uncertainty can be constructed at low computational effort. This min-max solution incurs various costs, called "empirical costs'', in correspondence of the sampled instances of the uncertain parameter. Our goal is to precisely characterize the risks associated to the empirical costs, namely to evaluate the probability that the various empirical costs are exceeded when a new uncertainty instance is seen. The main result is that the risks distribute as an ordered Dirichlet distribution, irrespective of the probability measure of the uncertain stochastic parameter. This provides a full-fledged characterization of the reliability of the min-max sample-based solution.



Thursday, 16:15 - 16:40 h, Room: MA 141, Talk 3

Alexei Gaivoronski
Stochastic bilevel optimization problems with applications to telecom

Coauthor: Paolo Pisciella


We consider several stochastic bilevel optimization problems which have applications to supply chain management and information economics, where the system under consideration is composed from several independent actors. We consider solution methods that utilize analysis of analytical properties of the problem with stochastic optimization techniques.


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