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Stochastic Optimization Methods for Large-Scale Machine Learning

   Cardiff School of Mathematics

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  Prof A Zhigljavsky, Dr JW Gillard  No more applications being accepted  Competition Funded PhD Project (UK Students Only)

About the Project

Many machine learning problems are formulated as non-convex optimization problems. For example, almost all the optimization problems in deep neural networks are non-convex. Non-convex optimization is one of the difficulties in the optimization problem. Unlike convex optimization, there may be innumerable optimum solutions in its feasible domain and the complexity of the algorithm for searching the globally optimal value is NP-hard.

Other problems include the presence of several local minima, which could trap a solution away from that which is globally optimal; inexact gradients, which force optimization methods to take incorrect routes in the hunt for the minimum; and the structure of the objective function, in that on a local scale the function could look rather different from how it does globally.

The aim of this work is to create new optimization methods which circumnavigate the above problems. Using previous work of the supervisors as a launch-pad, we will explore:

-         New, computationally efficient methods for estimating the gradient to inform the correct direction of travel for an iterative algorithm, which are provably robust to the presence of noise;

-         The design, implementation, and validation of novel global optimization algorithms to solve machine learning problems.

This project will be intradisciplinary, and you will expand your skill set by learning and combining the latest ideas from statistics, optimization, and linear algebra to develop exciting tools for users of machine learning. You will be exposed to solving a wide variety of meaningful real-world problems such as text-classification, image processing, clustering, which are widely used in industry. You will also learn how to program, and how to use the available software which implements the existing, classical techniques of machine learning. This project gives you the opportunity to work on the core of machine learning, an area which will only have increasing importance in our future lives.

Cardiff’s School of Mathematics provides an excellent postgraduate research environment. Project-specific academic training will be provided by the supervisors. The student will also benefit from the School’s excellent research culture, access to national course centres in mathematical training (MAGIC, APTS, NATCOR), the Doctoral Academy, which offers a comprehensive programme for postgraduate researchers to develop their professional skills, and the SIAM-IMA Student Chapter, a valuable forum for exchange and public engagement.

The training in this project opens up outstanding career prospects both in academia and industry.

Research Environment:

The School of Mathematics at Cardiff provides an excellent environment for a research student to develop professionally. The student will have an office space with their own computers in the newly build state-of-the-art ABACWS building which houses the School of Mathematics and the School of Computer Science and Informatics, providing the right environment to foster collaborations.  The supervisory team will support the research and professional development of the student. The student has access to nationwide centres with courses in mathematics (MAGIC), statistics (APTS) and Operations Research (NATCOR) and further professional development courses through the Doctoral Academy. Moreover, the School has five different research groups, each with individual seminars and School-wide Colloquia and interdisciplinary lectures as well as the Welsh Mathematics Colloquium which provide plenty of opportunities to mix with research leaders in different areas of Mathematics.

The School of Mathematics has a very active PGR student group which includes weekly PGR organized seminars, the SIAM-IMA Chapter and the Women in Mathematics group.  Academic staff in the School organize a number of workshops/conferences in Cardiff where students get the opportunity to network with leading researchers around the world.

Training and/or Development Opportunities:

This studentship is an outstanding opportunity to conduct cutting-edge research across disciplinary boundaries in Mathematics as part of an international team and in an excellent PGR environment on a topic of theoretical and practical importance.

To ensure the student is well-supported in all aspects of their research and personal development, the team will identify individual needs and provide project-specific training in at least weekly meetings. For academic training the student has access to three national course centres (MAGIC, APTS, NATCOR) that is complemented by the professional skills training of Cardiff's Doctoral Academy. The School’s research culture includes weekly seminars, global collaborations and an active participation in the Welsh Mathematics Colloquium, during which students gain first valuable feedback beyond their project team.

As the student progresses, they will learn how to disseminate their work in high-quality journals and during conferences enabling them to become part of a research community. In addition the SIAM-IMA Chapter provides a unique forum for public engagement. To further strengthen their CV, the student may gain teaching practice, whilst being mentored by an experienced lecturer.

How to apply:

Applicants should apply through the Cardiff University online application Mathematics - Study - Cardiff University, SIMS. Applicants should select Doctor of Philosophy in Mathematics, with a start date of October 2022. In the research proposal section of your application, please specify the project title “Stochastic Optimization Methods for Large-Scale Machine Learning” and supervisor/Lead supervisor “Prof Anatoly Zhigljavsky”.

In the funding section, please specify that you are applying for advertised funding.

Academic criteria:

A 1st or upper 2nd class UK Honours degree (or equivalent) and/or a Master’s degree is required in mathematics or a related subject.

Please upload the following supporting documents on SIMS :

·        Curriculum vitae

·        A personal statement

·        Two completed references

·        Degree certificates and transcripts

Deadline for applications:

27 May 2022


This studentship is available to home students.

Cardiff University is committed to supporting and promoting equality and diversity and to creating an inclusive environment for all. We welcome applications from all members of the global community irrespective of age, disability, sex, gender identity, gender reassignment, marital or civil partnership status, pregnancy or maternity, race, religion or belief and sexual orientation.

Short-listed applicants will be invited to interview w/c shortly after the application deadline.

As part of the interview process, applicants will be asked to answer a series of questions by a panel of academics.

Interviews are expected to take place remotely via Zoom/Teams on within one month after the application deadline.

Funding Notes

The School of Mathematics at Cardiff University is delighted to offer a fully funded studentship starting in October 2022.

How good is research at Cardiff University in Mathematical Sciences?

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