We investigate algorithms for different steps in the decision making process, focusing on systems where we are uncertain about the outcomes but can quantify how probable they are using random variables. Any decision one makes in such a situation leads to a distribution of outcomes and requires a way to evaluate a decision. The standard approach is to marginalise the distribution of outcomes into a single number that tries in some way to summarise the value of each decision. After selecting a marginalisation approach, mathematicians and decision makers focus their analysis on the marginalised value but ignore the distribution. We argue that we should also be investigating the implications of the chosen mathematical approach for the whole distribution of outcomes. We illustrate the effect different mathematical formulations have on the distribution with one-stage and sequential decision problems. We show that different ways to marginalise the distributions can result in very similar decisions but each way has a different complexity and computational cost. It is often computationally intractable to approximate optimal decisions to high precision and much research goes into developing algorithms that are suboptimal in the marginalised sense, but work within the computational budget available. If the performance of these algorithms is evaluated they are mainly judged based on the marginalised values, however, comparing the performance using the full distribution provides interesting information: We provide numerical examples from dynamic pricing applications where the suboptimal algorithm results in higher profit than the optimal algorithm in more than half of the realisations, which is paid for with a more significant underperformance in the remaining realisations. All the problems discussed in this thesis lead to continuous optimisation problems. We develop a new algorithm that can be used on top of existing optimisation algorithms to reduce the cost of approximating solutions. The algorithm is tested on a range of optimisation problems and is shown to be competitive with existing methods.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:757928 |
| Date | January 2018 |
| Creators | Riseth, Asbjørn Nilsen |
| Contributors | Dewynne, Jeff ; Farmer, Chris |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://ora.ox.ac.uk/objects/uuid:a66e17dc-a626-4226-82f6-2d716f8690fd |
Page generated in 0.002 seconds