Buet-Golfouse, Francois;
(2024)
New Mathematical and Computational Methods for Machine Learning and Multi-Objective Reinforcement Learning.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
This thesis concerns various aspects of robustness in machine learning, which refers broadly to the impact of certain modelling assumptions on a model’s quality. The topic is examined from various perspectives, ranging from theoretical statistics to applied modelling. The main message of the six chapters is that problem framing and the probabilistic properties of algorithms used in data science are crucial for inferring robust insights from data and models. The first part discusses two machine learning applications: classification and recommender systems. It answers an open question about the type of aleatoric uncertainty supporting the principle of margin maximisation for classification, establishing that heavy-tailed distributions do not fit this framework under certain conditions. For recommender systems, the focus is on designing a flexible method that can be applied to a range of use cases while being economical in terms of parameters, particularly for small and large datasets. The second part focuses on fairness in machine learning, exploring situations where there are trade-offs between objectives such as accuracy and equal opportunities for different groups based on protected characteristics. A framework based on probably approximately correct learning is proposed to address the challenge of generalising to new data, and group functionals are suggested as a simple approach to fairness in unsupervised learning algorithms. The third and final part considers situations where agents must optimise multiple conflicting objectives. New reinforcement learning and multi-armed bandit algorithms are proposed, allowing agents to learn policies over the space of trade-offs. The thesis also explores the idea that an agent’s preferences may change over time, which is particularly relevant to economic and financial problems such as optimal trade execution.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | New Mathematical and Computational Methods for Machine Learning and Multi-Objective Reinforcement Learning |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2022. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10186904 |
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