Making decisions with pareto fronts under uncertainty
File(s)
Author(s)
Tu, Ben
Type
Thesis
Abstract
Many problems in the real-world can be formulated as a multi-objective optimisation problem. The conventional goal of this problem is to identify the best set of decisions which lead to the best set of outcomes: namely, the Pareto front of the problem. To solve these multi-objective problems in practice, it is common for modern-day practitioners to take a more data-driven approach. That is, an approach wherein one actively collects observational data in order to approximately identify the decisions which benefit the decision makers the most. Naturally, as with any data-driven procedure, there are many different sources of uncertainty that could potentially enter into this process---some inadvertent, some unavoidable. The purpose of this thesis is to develop the framework and tools required to perform this procedure effectively and principally in the face of these uncertainties. To that end, we begin this work by reformulating this entire multi-objective decision making procedure under the lens of Bayesian decision theory. Equipped with this viewpoint, we then try to extend and consolidate the relevant methodologies that are required in order to operate within this probabilistic regime. Notably, each of the main chapters of this thesis is dedicated to solving some aspect of this task.
Version
Open Access
Date Issued
2024-09-11
Date Awarded
01/01/2025
License URL
Advisor
Kantas, Nikolas
Gandy, Axel
Sponsor
Engineering and Physical Sciences Research Council
BASF
Grant Number
EP/S023151/1
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)