Dynamic Decision Making

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

This course is designed to provide a basic understanding of dynamic decision making (DM) under uncertainty and related tools. It is expected that students will learn how to formulate DM problem and to solve it using the technique described. The course also introduces a basic of Fully Probabilistic Design (FPD), which is a non-trivial extension of Bayesian DM. The course offers a unified view on stochastic filtration and dynamic programming, as well as a conceptually feasible construction of respective probabilistic description, and elements of multiple-participant DM. The course will be illustrated by examples of real applications.

Requirements:

This course is appropriate for graduate students (Master's or PhD level) who are focused on research and development in the areas employing dynamic DM under uncertainty, for e.g. stochastic and adaptive control; learning; optimisation; AI; forecasting; fault detection and isolation; pattern recognition, and other. Students with varied backgrounds (incl. natural and social sciences science, engineering, economics, etc.) are welcome.

Syllabus of lectures:

Section 1 - Basic theory: Introduction to DM; General Conventions & Basic Notions; Ordering of Behaviours; Complete Ordering of Strategies; Calculus with Probability Densities (Pd) and with Expectation; Behaviour and Its Parts; Decomposition of Decision Making. Section 2- Bayesian DM: Basic DM Lemma; Dynamic DM Design; Bayesian Filtering and Estimation; Asymptotic of the Design and of the Estimation Section 3- Fully Probabilistic Design (FPD) and Its Elements: Motivation and Solution; General FPD; FPD and Traditional Design; Leave to the Fate Option; Approximation of Pds; Principle of minimum Kullback-Leibler divergence; Extension of Non-Probabilistic Knowledge; Merging of Incompletely Compatible Pds; Need for Approximation & Possible Solutions. Section 4 - Practical Aspects: Feasible and Approximate Learning and Design; DM Elements and Basic Types of DM; Estimation in Exponential Family; Equivalence Approach; Estimation with Forgetting; Feasible and Approximate Design; Suboptimal Design; Strategies Simplifying Models & Optimisation Space; Knowledge And Preference. Elicitation Section 5 - DM with Multiple Imperfect Participants:Introduction to Multi-participant DM; Participants' Imperfectness; Related Tasks; Cooperation within FPD

Syllabus of tutorials:

Study Objective:

Study materials:

M. Karny, J. Bohm, T.V. Guy, L. Jirsa, I. Nagy, P. Nedoma, and L. Tesar. Optimized Bayesian Dynamic Advising: Theory and Algorithms. Springer, London, 2006. M. Karny and T.V. Guy. Fully probabilistic control design. Systems & Control Letters, 55(4), 2006. M. Karny and T.V. Guy. On support of imperfect bayesian participants. In: T.V. Guy, M. Karny, and D.H. Wolpert, Eds, Decision Making with Imperfect Decision Makers, volume 28, Springer, Berlin, 2012. M. Karny 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: