New Mathematical and Computational Methods for Machine Learning and Multi-Objective Reinforcement Learning - Dissertation

Aug 4, 2026

Uploaded by Aria

This PhD dissertation studies robustness in machine learning, focusing on how modelling assumptions and probabilistic properties of learning algorithms shape predictive quality. It addresses robustness through margin maximisation for classification and through flexible, parameter-economical modelling for recommender systems, including heavy-tailed regimes. It also develops fairness-focused frameworks for learning and generalisation under protected group constraints. Finally, it proposes multi-objective reinforcement learning and multi-armed bandit methods for agents whose preferences may evolve, with applications such as optimal trade execution.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages171

Reading Time7 h 11 min

AccessFree to download

Abstract

Robustness: classification and recommender systems

Fairness: trade-offs and group-based learning

Multi-objective optimisation: reinforcement learning and bandits

Impact Statement

Academic contributions

Practical implications

New Mathematical and Computational Methods for Machine Learning and Multi-Objective Reinforcement Learning Francois Buet-Golfouse A dissertation submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy of University College London. Department of Mathematics University College London February 8, 2024 2 I, Francois Buet-Golfouse, conﬁrm that the work presented in this thesis is my own. Where information has been derived from other sources, I conﬁrm that this has been indicated in the work. 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. Impact Statement The research presented in this thesis addresses critical issues in machine learning from the perspectives of robustness, fairness, and multi-objective optimisation. The work offers novel insights into the underlying principles of machine learning algorithms and provides practical solutions to mitigate the negative impact of biased or suboptimal models on individuals and communities. The ﬁrst part of the thesis focuses on robustness in machine learning, speciﬁcally in the context of margin maximisation in classiﬁcation algorithms. The work highlights the importance of tail distributions and loss function properties in this optimisation process and shows that margin maximisation applied to heavy-tailed distributions can lead to suboptimal performance. The thesis also introduces anew class of models, kernel factorisation machines, which can effectively ﬁt ﬂexible recommender systems with fewer parameters, addressing both small-and big-data contexts. The second part of the thesis deals with fairness in machine learning, which is essential for building ethical and trustworthy systems that can beneﬁt everyone equally. The research proposes a disciplined methodology for tackling bias in unsupervised learning algorithms and investigates the challenges of checking machine learning algorithms for fairness and correcting possible biases. The work also provides theoretical guarantees on out-of-sample generalisation, thus ensuring that the proposed algorithms can be applied to real-world problems with conﬁdence. The ﬁna

FAQs

What does the thesis mean by robustness in machine learning?

Robustness refers to how modelling assumptions affect a model’s quality and reliability. The thesis studies robustness from both theoretical statistics and applied modelling perspectives.

How is fairness addressed in the thesis?

The thesis investigates trade-offs between objectives such as accuracy and equal opportunities across groups defined by protected characteristics. It proposes learning-based frameworks for generalisation to new data and suggests group functionals for fairness in unsupervised learning.

What multi-objective methods does the thesis propose for reinforcement learning?

It proposes new reinforcement learning and multi-armed bandit algorithms that let agents learn policies across trade-offs between conflicting objectives. It also considers changing agent preferences over time, motivated by economic and financial decision problems.

Aug 4, 2026

Uploaded by Aria