Decentralised sequential decision making and learning

Many modern sequential decision-making tasks involve multiple decision-makers working in parallel. Often, this is to distribute workload or the requirement to serve multiple users at once. Additionally, the decision-makers, whom we call agents, can work collaboratively to solve their tasks more efficiently. An example of such a problem is that of a webserver needing to dynamically select an advertisement to be displayed each time a page is requested. Popular websites will often require multiple webservers to handle many users in parallel and in different geographical locations. Ideally, the webservers should share some data so they learn which ads are best to show as fast as possible.
The multi-agent multi-armed bandit problem provides a theoretical framework that can be used to model such problems and to devise such algorithms for them. Additionally, it allows us formally reason about this problem so we can prove theoretical results. My research involves developing algorithms for this framework that are both decentralised and communication constrained. These algorithms will be justified using theoretical and numerical results.
The development of such algorithms that are decentralised and communication constrained is useful for many reasons. Firstly, decentralisation makes the network of agents easily scalable and tolerant of potentially faulty agents. Secondly, there may be geographical constraints that prevent sharing large amounts of data, Finally, reducing the amount of data being shared in a network could decrease electricity consumption.
My research will focus on two extensions of the multi-agent multi-armed bandit problem. Firstly, we will consider the case where the set of actions is the continuum. This may arise in an application where we want to maximise the yield from a chemical reaction where we can control the temperature. In this example, there is some structure to the actions. Similar temperatures should give similar yields. Therefore, in this setting, we also make the natural assumption that the rewards are generated by a Hölder-continuous function with some noise. Secondly, we will consider the case of a non-stationary environment. Here we allow the unknown rewards distributions of each action to change over time. This naturally occurs in many applications, for example, consider dynamically selecting advertisements for a website, At different points in time, certain advertisements may perform depending on how whether their product is currently trending. For both settings, the goal is to devise novel algorithms with tight theoretical guarantees. This will involve building on top of existing literature from the single-agent setting of the multi-armed bandit problem and developing many new ideas.

The COMPASS Centre for Doctoral Training will have the following impact.

Doctoral Students Impact.

I1. Recruit and train over 55 students and provide them with a broad and comprehensive education in contemporary Computational Statistics & Data Science, leading to the award of a PhD. The training environment will be built around a set of multilevel cohorts: a variety of group sizes, within and across year cohort activities, within and across disciplinary boundaries with internal and external partners, where statistics and computation are the common focus, but remaining sensitive to disciplinary needs. Our novel doctoral training environment will powerfully impact on students, opening their eyes to not only a range of modern technical benefits and opportunities, but on the power of team-working with people from a range of backgrounds to solve the most important problems of the day. They will learn to apply their skills to achieve impact by collaborative working with internal and external partners, such as via our Rapid Response Teams, Policy Workshops & Statistical Clinics.

I2. As well as advanced training in computational statistics and data science, our students will be impacted by exposure to, and training in, important cognate topics such as ethics, responsible innovation, equality, diversity and inclusion, policy, effective communication and dissemination, enterprise, impact and consultancy skills. It is vital for our students to understand that their training will enable them to have a powerful impact on the wider world, so, e.g., AI algorithms they develop should not be discriminatory, and statistical methodologies should be reproducible, and statistical results accurately and comprehensibly communicated to the general public and policymakers.

I3. The students will gain experience via collaborations with academic partners within the University in cognate disciplines, and a wide range of external industrial & government partners. The students will be impacted by the structured training programmes of the UK Academy of Postgraduate Training in Statistics, the Bristol Doctoral College, the Jean Golding Institute, the Alan Turing Institute and the Heilbronn Institute for Mathematical Sciences, which will be integrated into our programme.

I4. Having received an excellent training, the students will then impact powerfully on the world in their future fruitful careers, spreading excellence.

Impact on our Partners & ourselves.

I5. Direct impacts will be achieved by students engaging with, and working on projects with, our academic partners, with discipline-specific problems arising in engineering, education, medicine, economics, earth sciences, life sciences and geographical sciences, and our external partners Adarga, the Atomic Weapons Establishment, CheckRisk, EDF, GCHQ, GSK, the Office for National Statistics, Sciex, Shell UK, Trainline and the UK Space Agency. The students will demonstrate a wide range of innovation with these partners, will attract engagement from new partners, and often provide attractive future employment matches for students and partners alike.

Wider Societal Impact

I6. COMPASS will greatly benefit the UK by providing over 55 highly trained PhD graduates in an area that is known to be suffering from extreme, well-known, shortages in the people pipeline nationally. COMPASS CDT graduates will be equipped for jobs in sectors of high economic value and national priority, including data science, analytics, pharmaceuticals, security, energy, communications, government, and indeed all research labs that deal with data. Through their training, they will enable these organisations to make well-informed and statistically principled decisions that will allow them to maximise their international competitiveness and contribution to societal well-being. COMPASS will also impact positively on the wider student community, both now and sustainably into the future.