Generative Models for Large-Scale Combinatorial Decision-Making

The UKRI AI Centre for Doctoral Training (CDT) in Decision Making for Complex Systems is a joint CDT between The University of Manchester and the University of Cambridge. The CDT provides funding for four years of advanced studies towards a PhD. The first year consists of a taught program at Manchester that will cover the fundamentals of Machine Learning. This year is followed by three years of research at either at Manchester or Cambridge. Please note the research element of the PhD will take place at the host institution of the supervisor listed for each project.

Combinatorial Decision-Making– where the maxima or minima of an objective function acting on a finite set of discrete variables is sought – has attracted significant interest in many studies on decision-making for complex systems due to both their (often NP) hard nature and numerous practical applications across domains varying from logistics, physics, material science to fundamental sciences. As the search space of feasible solutions typically grows exponentially with the problem size, exact solvers can be challenging to scale; hence, combinatorial decision-making problems are often tackled with handcrafted heuristics using expert knowledge, which, however, are often hard to devise even for experienced domain experts.

Generative Models (GMs), including Large Language Models (LLMs) such as ChatGPT/GPT4 and diffusion models such as Dalle2, allow AI to generate images/text, write code, generate synthetic data and naturally interact with a computer. Whilst the highest profile applications of GMs have been in text and images [1], this project seeks to improve their utility in combinatorial decision-making problems to enable the capture of the delicate characteristics of handcrafted heuristics from expert knowledge [2].

Specifically, this project tackles the following significant research challenges: (1) modelling of graph-structured distributions: combinatorial optimization problems are usually described in the form of graphs, with nodes and edges corresponding to the discrete variables. This graph-structured distribution will pose a great challenge for modelling the heuristics with the generative models since the latter focuses primarily on vector distributions; (2) training efficiency for large-scale problems: As the problem size increases, solving for even feasible (not optimal) solutions with the heuristic methods will be slow and computationally expensive. This will be exacerbated by the even more computationally intensive training of generative models; and (3) expert-in-the-loop learning: capturing the heuristics using expert knowledge inevitably requires the expert in the loop for the training. Ensuring that models align with expert values and learn the effective heuristics for solution construction will need a more delicate design of the generative sampling process. 

Entry requirements

Applicants should have, or expect to achieve, at least a 2.1 honours degree or a master’s (or international equivalent) in a relevant science or engineering related discipline.

How to Apply

As the CDT has only recently been awarded we strongly encourage you to contact the supervisor of the project you are interested in with your CV and supporting documents. You will have a chance to meet with prospective supervisors prior to submitting an application – further details will be provided.

Equality, diversity and inclusion is fundamental to the success of The University of Manchester, and is at the heart of all of our activities. We know that diversity strengthens our research community, leading to enhanced research creativity, productivity and quality, and societal and economic impact.

We actively encourage applicants from diverse career paths and backgrounds and from all sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation and transgender status.

We also support applications from those returning from a career break or other roles. We consider offering flexible study arrangements (including part-time: 50%, 60% or 80%, depending on the project/funder).

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