Dynamic Decision Making

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Requirements:

Basic courses of mathematical analysis, statistics and algebra; ideally, control theory

Syllabus of lectures:

Basic theory: Introduction to decision making (DM); general conventions and notions; behavior and its parts; decomposition of DM; ordering of behaviors and strategies;

Bayesian DM: Basic DM Lemma; dynamic DM Design; Bayesian filtering and estimation; asymptotic of the design and of the estimation.

Fully Probabilistic Design (FPD): formulation and solution; FPD and traditional DM; principle of probability density approximation; principle of minimum Kullback-Leibler divergence; extension of non-probabilistic knowledge; merging of incompletely compatible probability densities; need for approximation.

Practical Aspects: feasible and approximate learning; DM elements and basic DM types; estimation in exponential family; estimation with forgetting; feasible and approximate design; simplified models and optimization spaces; knowledge and preference elicitation.

DM with Multiple Imperfect Participants: introduction to multi-participant DM; imperfectness of participants; cooperation of participants.

Syllabus of tutorials:

Study Objective:

This course provides a basic understanding of dynamic decision making (DM) under uncertainty and related tools. The students will learn how to formulate and solve DM problems using the described methodology. The course also introduces a non-trivial extension of Bayesian DM called Fully Probabilistic Design (FPD). The course offers a unified view on stochastic filtration and dynamic programming. It introduces a conceptually feasible construction of respective probabilistic description, and elements of multi-participant DM. The course content is illustrated by examples of real applications.

Study materials:

[1] M. Kárný, J. Bohm, T.V. Guy, L. Jirsa, I. Nagy, P. Nedoma, and L. Tesař. Optimized Bayesian Dynamic Advising: Theory and Algorithms. Springer, London, 2006.

[2] M. Kárný and T.V. Guy. Fully probabilistic control design. Systems & Control Letters, 55(4), 2006.

[3] M. Kárný and T.V. Guy. On support of imperfect Bayesian participants. In: T.V. Guy, M. Kárný, and D.H. Wolpert, Eds, Decision Making with Imperfect Decision Makers, volume 28, Springer, Berlin, 2012.

[4] M. Kárný and T. Kroupa. Axiomatisation of fully probabilistic design. Information Sciences, 186(1), 2012.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Matematické inženýrství (elective course)
• Aplikace softwarového inženýrství (elective course)