Unit name | Stochastic Optimisation |
---|---|
Unit code | MATHM6005 |
Credit points | 10 |
Level of study | M/7 |
Teaching block(s) |
Teaching Block 2C (weeks 13 - 18) |
Unit director | Dr. Tadic |
Open unit status | Not open |
Pre-requisites |
None |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Stochastic optimisation covers a broad framework of problems at the interface of applied probability and optimisation. The main focus of this unit is on Markov decision processes and game theory. Markov decision processes describe a class of single decision-maker optimisation problems that arise when applied probability models (eg Markov chains) are extended to allow for action-dependent transition distributions and associated rewards. Game theory problems are more complex in that they involve two or more decision makers (players), so the optimal action for each player will depend on the actions of other players. Here, we focus on Nash equilibria - strategies that are conditionally optimal in the sense that a player can not do do better by changing their own strategy while other players stay with their current strategy.
Aims
The underlying aim is to use a combination of models, techniques and theory from stochastic control and equilibrium selection to determine behaviour that is optimal with regard to some given reward structure.
Syllabus
Relation to Other Units
This unit is a first course on stochastic optimisation.
Students who successfully complete this unit should be able to:
Transferable Skills:
In addition to the general skills associated with other mathematical units, students will also have the opportunity to gain practice in the following: report writing, oral presentations, use of information resources, use of initiative in learning material in other than that provided by the lectures themselves, time management, general IT skills and word-processing.
Lectures, supported by problem sheets, problems classes and solution sheets.
The assessment mark for Stochastic Optimisation is calculated from a 1½-hour written examination in APRIL consisting of THREE questions. A candidate's best TWO answers will be used for assessment. Calculators of an approved type (non-programmable, no text facility) are allowed.