Multi-objective decision making.

Making decisions in the real world is difficult because there are usually many perspectives and options to consider simultaneously. Many of these problem can be formalised mathematically as a type of multi-objective decision making problem, where the goal is to identify a set of decisions that offer the best compromise among the different objectives set by the decision maker. The focus of this project is to develop theoretically justified algorithms to solve different types of multi-objective decision making problems. This project falls within the EPSRC Mathematical Sciences research area, which covers relevant areas such as "operational research" and "statistics and applied probability". This project is also supported by the multinational chemical company BASF, whose collaboration will help drive the development and testing of tools that are both effective and practical in purpose.

A central part of this project is focussed on the multi-objective black-box optimization problem, where the goal is to optimize a vector valued function that is expensive to evaluate and subject to noise. For example, a common problem in chemical manufacturing is to find the combination of controls inputs that lead to some desirable performance outcomes such as high yield and low economical cost. In such a setting, we might not fully understand the possible chemical reactions that can take place and hence we rely solely on the data collected by the technicians performing the chemical experiments. Bayesian optimization has been shown in the literature to be a promising strategy to address these sorts of problems. This work will build on top the existing literature and focus on building effective models and utility functions that take into consideration the multi-objective and sequential nature of the problem. In particular, a practical extension to the existing work is to improve sample efficiency of the optimization procedure by effectively and efficiently incorporating correlation between the objectives and the dynamics of the sequential selection procedure.
The other direction of this work considers the more general problem, which falls under the topic of multi-objective Markov decision processes. These processes are commonly used to model a sequential decision making problem, where a decision maker interacts with a system sequentially in time by selecting actions. The actions that a user takes influences the feedback they receive from the system and the potential feedback they will receive in the future. A large portion of the existing work for the multi-objective feedback setting relies on the scalarization framework, where we transform the multi-objective problem into a set of single objective problems that can be solved using standard techniques. The development of theoretical results for solving these multi-objective problems with and without scalarization is still an ongoing endeavour. This project will contribute to this effort by identifying and addressing gaps in the literature where feasible. The hope is that this stream of work will uncover some useful insight, which can then be exploited to create multi-objective algorithms that are supported by theoretical guarantees.

The primary CDT impact will be training 75 PhD graduates as the next generation of leaders in statistics and statistical machine learning. These graduates will lead in industry, government, health care, and academic research. They will bridge the gap between academia and industry, resulting in significant knowledge transfer to both established and start-up companies. Because this cohort will also learn to mentor other researchers, the CDT will ultimately address a UK-wide skills gap. The students will also be crucial in keeping the UK at the forefront of methodological research in statistics and machine learning.
After graduating, students will act as multipliers, educating others in advanced methodology throughout their career. There are a range of further impacts:
- The CDT has a large number of high calibre external partners in government, health care, industry and science. These partnerships will catalyse immediate knowledge transfer, bringing cutting edge methodology to a large number of areas. Knowledge transfer will also be achieved through internships/placements of our students with users of statistics and machine learning.
- Our Women in Mathematics and Statistics summer programme is aimed at students who could go on to apply for a PhD. This programme will inspire the next generation of statisticians and also provide excellent leadership training for the CDT students.
- The students will develop new methodology and theory in the domains of statistics and statistical machine learning. It will be relevant research, addressing the key questions behind real world problems. The research will be published in the best possible statistics journals and machine learning conferences and will be made available online. To maximize reproducibility and replicability, source code and replication files will be made available as open source software or, when relevant to an industrial collaboration, held as a patent or software copyright.