A Stackelberg game is a hierarchical game of two players known as the leader (upper-level player) and follower (lower-level player). One of the key characteristics of a Stackelberg game is that it involves an order of play, which assumes that the leader makes the first move, and after observing the choice of the upper-level player, the follower reacts by selection an action that optimizes their payoff function. The decision of the follower could be in favour of the leader, which would imply that there is cooperation between the two players. However, if the lower-level player's action is not in favour of the leader, we have a non-cooperative Stackelberg game. Overall, this means that to numerically solve a Stackelberg problem, we typically need to be in one of the following four categories: (A) The implicit function model, where the follower has only a single choice for each decision of the leader. (B) The optimistic model, where the follower could have multiple options for some actions of the leader, but nevertheless makes choices that are in favour of the upper-level player. (C) The pessimistic model, in which the follower is in a position where they could have multiple options for some selections of the leader and decides to make choices that do not favour the leader. (D) The partial cooperation model, which is also based on the assumption that the follower has multiple options for some selections of the leader, but with the difference that both players make a compromise with choices that are not necessarily their best ones, in order to let the other player partially satisfied. In the last 10 to 15 years, there has been an exponential rise of applications of Stackelberg games in the field of machine learning. Overwhelmingly, the theoretical and algorithmic developments have relied on category (A) above. However, the basic assumption required for this category is that the follower only has a unique choice for any decision made by the leader. This is too strong, and obviously, implies that there is no freedom of choice for the lower-level player. This framework is not feasible for many machine learning problems. For example, in adversarial learning, where a major concern is that data used for training a model could be attacked by a malicious agent to achieve a prediction goal that is not necessarily the one that the corresponding classification task would genuinely lead to, it does not make sense to assume that any of the players would make choices that would favour the other, whether the leader (resp. follower) is that training model (resp. malicious agent) or vice-versa, as both viewpoints are possible and have been considered in the literature. Clearly, in such a case, categories (C) and (D) seem to be more tractable. More broadly, in the current literature, not much attention has been dedicated to thoroughly assess the implications of categories (A)-(D) for Stackelberg game-based machine learning problems. A consequence of this is that potentially, existing algorithms could lead to decision-making that does not accurately reflect the modelling reality. Therefore, the overall goal of this project is to conduct a feasibility study that will lead to a framework to develop powerful algorithms to solve machine learning problems that are based on the Stackelberg game paradigm. To achieve this goal, we organize the work around four objectives; i.e., (1) conduct a detailed survey on applications of Stackelberg games in machine learning; (2) study the practical validity of categories (A)-(D) in the context of Stackelberg games in machine learning; (3) construct categories for Stackelberg models in machine learning (including existence results) and build the corresponding single-level reformulations; and (4) based on the analysis from the previous three objectives, build the first draft of a grant proposal to fund an extensive study to develop powerful algorithms for Stackelberg programs in machine learning.

Generative Models are AI models that can generate data. Recently researchers have shown that by training these models on large amounts of data (text data from the internet and images) these models learn to understand the regularities of our text and image world so well that they can generate responses to questions and create new images with surprising fidelity. This heralds a new era in which computers can assist humans to carry out tasks more efficiently than ever with significant opportunities for society, science and industry. However, these advances need significant research still -- how to make them train efficiently on different problems, how to understand their reliability and adherence to ethical norms.

Chemical biology is spearheading the development & translation of novel molecular tools and technologies to study biology and develop biomedical understanding. Dovetailing these platforms with industry 4.0/5.0 breakthroughs in automation & robotics, artificial intelligence & machine learning, the CDT will unlock the Lab of the Future paradigm. This will redefine the state of the art with respect to making, measuring, modelling & manipulating molecular interactions in biological systems, leading to novel R&D workflows, promoting efficient design-test cycles and driving sustainability. These molecular technologies will (i) enable biological & medical research, (ii) revolutionise understanding of disease & (iii) create novel diagnostics, drugs & therapies, focusing increasingly on individual patient outcomes. They will also impact the agri-tech sector which faces huge demand to increase productivity by unlocking strategies to e.g. track agrochemicals in plants/soil, understand modes of action & drive precision farming. Similarly, advances in personal care industrial processes are critically dependent on development of molecular technologies to gain insight into structured product design. The application of novel molecular tools/technologies, Lab of the Future strategies & their commercialisation through the instrumentation science sector is thus critical to the UK economy, supporting >4,500 healthcare, personal care, agri-science & biotech companies. This will transform (i) therapeutic, agrochemical & personal care product discovery (ii) med-tech/biotech/healthcare instrumentation R&D pipelines & (iii) stimulate creation of SMEs. Working closely with civic partners including Hammersmith & Fulham Council and the NHS, the CDT's talent & research pipeline will act as a growth engine for one of the most rapidly expanding Life Science ecosystems in Europe, the White City Innovation District. Given the importance of Chemical Biology to UK plc there is great demand but short supply of Chemical Biology PhD graduates able to match the pace of innovation across the physical/life science interface, at a time when industry & health sectors need these skills to accelerate productivity. The CDT in Chemical Biology: Empowering UK BioTech innovation with its unique 5 year programme: 1 year MRes + 3 year PhD + 1 year ELEVATE Fellowship directly addresses this skills gap by training a new generation of career-ready graduates, able to embrace the Lab of the Future concept and unlock its potential by fusing innovative molecular tools & tech with industry 4.0 & 5.0 advances to study molecular interactions & develop applications in the life science, agriscience & personal care sectors. CDT students will benefit from a research and training programme created with >100 industry/external stakeholders designed to meet future employer's needs. Our cohort-based programme with EDI at its heart, will allow students to contextualise their work within wider CDT activities & find novel solutions to their research, supported by one of the world's largest Chemical Biology communities: the Institute of Chemical Biology (>165) research groups. Students will be trained in multidisciplinary blue skies/translational research, lean innovation, scale fast/fail fast approaches, creating scientists able to understand molecular technologies, sustainable product design, early-stage commercialisation, & industry's pace of change. To support this, our training includes Future Lab & HackEDU courses (prototyping training), a drug screening programme, Biz-Catalyst (entrepreneurial training), InnovaLab (SME accelerator), a Data Science course, Human Centred Design, Science Communication (with BBC) & Bioethics/RRI/Sustainability/Policy courses. Following PhD completion, students can enter the ELEVATE fellowship programme, bridging the gap between PhD & industry/academia, offering training, personalised workplace opportunities & enable students to kickstart new companies.