Contributed Session Thu.2.MA 144

Thursday, 13:15 - 14:45 h, Room: MA 144

Cluster 22: Stochastic optimization [...]

Large-scale and multi-stage stochastic optimization


Chair: Alois Pichler



Thursday, 13:15 - 13:40 h, Room: MA 144, Talk 1

Anna Timonina
Multi-stage stochastic optimisation and approximations with applications


Multi-stage stochastic optimization problems play a very important role in management of financial portfolios, energy production, insurance portfolios etc. The exact analytical solution for such problems can be found only in very exceptional cases and the necessity of an approximation arises immediately. The aim of this research is to study the approximation of the stochastic process by the probability valued finite tree. We use the concept of nested distribution to describe the information structure keeping the setup purely distributional and the concept of nested distance to measure the distance between nested distributions and to quantify the quality of approximation. We introduce the algorithm for calculating the nested distance between tree and stochastic process given by its distribution. Minimization of this distance can lead to the new method for generating values from some specific distribution along with Monte Carlo generating and Optimal Quantization. The main advantage of this algorithm is that it takes into account conditional distributions at each stage, that allows to approximate a large class of processes.



Thursday, 13:45 - 14:10 h, Room: MA 144, Talk 2

Jose Nino-Mora
Sufficient indexability conditions for real-state restless bandit projects via infinite-dimensional LP-based partial conservation laws


The multiarmed restless bandit (RB) problem concerns the optimal dynamic allocation of a shared resource to multiple stochastic projects, modeled as RBs, i.e., binary-action (active/passive) Markov decision processes. Although the problem is generally intractable, a unified approach to construct heuristic policies based on the Whittle priority index, or extensions thereof, has been shown to perform well in a variety of models. Deploying such an approach requires to establish the indexability (i.e., existence of the index) for the constituent RBs, and to evaluate the index numerically. This work presents the first general sufficient conditions for indexability of real-state RBs, motivated by applications that have drawn recent research attention. The conditions are based on an infinite-dimensional LP extension of partial conservation laws, an approach formerly introduced by the author to provide sufficient indexability conditions for discrete-state RBs. The approach further provides a practical means to evaluate the index. Applications will be discussed.



Thursday, 14:15 - 14:40 h, Room: MA 144, Talk 3

Alois Pichler
Approximation of stochastic processes


We deal with extremely large scale and high dimensional optimization, where managerial decisions are allowed at consecutive instants of time. Scenarios, reflecting future states of the world, are considered random. It is well known how to deal with these types of stochastic optimization problems with an expectation in the objective, but we want to additionally address risk.
The newly introduced notion of a process distance (Pflug) allows quantifying approximations. We address approximations, which allow reasonable computation times and give viable bounds in comparison to the original problem. The results are general enough to involve risk measures, which (historically) appeared first in finance and insurance.
Finally the approximating processes can be improved by different means to improve their approximating quality


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