Modelling of Stochastic Dynamic Systems and Algorithms for Solving Markov Decision Problems

Programmee:International Collaboration
Code:STCU 5988
Execution period:2015 – 2016
Institutions:Institute of Mathematics and Computer Science
Project Leader:Lozovanu Dmitrii
Participants: Mishkoy Gheorghe, Kolesnik Alexander, Naval Elvira, Alexandru Lazari, Maria Capcelea


This research project is concerned with studying a class of stochastic dynamic decision models that comprises stochastic versions of classical discrete optimal control problems, discrete Markov decision processes and stochastic positional games with average and discounted payoffs. The aim of the project is to develop efficient methods and numerical algorithms for determining the solutions of the considered decision problems with finite and infinite time horizon. This class of problems we formulate and study using the recent results of optimization theory, the modern concept of Markov decision processes and the game-theoretical approach to such processes. Based on such concept and approaches we plan to elaborate new algorithms for solving the mentioned stochastic dynamic decision problems and to extend the algorithms for new classes of problems that generalize classical ones.

The basic theoretical results we expect are concerned with the existence of the solutions for the considered class of problems and the correctness of the proposed algorithms. For the stochastic positional games with average and discounted payoffs new conditions for existence of Nash equilibria will be derived and algorithms for determining the optimal stationary strategies of the players will be proposed and grounded. Additionally the antagonistic stochastic positional games will be studied and the algorithms for determining saddle points will be proposed. The elaborated algorithms will be estimated from computational point of view and implemented in the corresponding software environment. Some possible applications of the considered stochastic dynamic decision models will be analyzed. In particular we will apply the proposed models and approaches for studying some of the economic growth models and Shapley stochastic games.