MA333      Half Unit
Optimisation for Machine Learning

This information is for the 2022/23 session.

Teacher responsible

Prof Laszlo Vegh COL 2.02


This course is available on the BSc in Business Mathematics and Statistics, BSc in Data Science, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.


Students must be familiar with the fundamentals of continuous optimisation, to the level in Optimisation Theory (MA208) or equivalent.

Course content

Machine learning uses tools from statistics, mathematics, and computer science for a broad range of problems in data analytics. The course introduces a range of optimisation methods that play fundamental roles in machine learning. This is a proof-based course that focuses on the underlying mathematical models and concepts.

Basic tools from convex analysis. Lagrangian duality and Karush-Kuhn-Tucker conditions. First-order methods and convergence guarantees, including conditional gradient descent and stochastic gradient descent. Quadratic programming, support vector machines. Online convex optimization, online gradient and multiplicative weight methods. Second-order optimization: Newton’s method.


This course is delivered through a combination of classes and lectures totalling a minimum of 32 hours across Lent and Summer term. 

Formative coursework

Students will be expected to produce 8 exercises in the LT.

Written answers to set problems will be expected on a weekly basis.

Indicative reading

  • Vishnoi, N. (2018). Algorithms for Convex Optimization (2021). Cambridge University Press.
  • Boyd, S., & Vandenberghe, L. (2004). Convex optimization. Cambridge University Press.
  • Nesterov, Y. (2018). Lectures on convex optimization (Vol. 137). Springer.
  • B. Gärtner and M. Jaggi. Optimization for machine learning (lecture notes), 2021.
  • E. Hazan. Introduction to online convex optimization (lecture notes), 2021.


Exam (90%, duration: 2 hours) in the summer exam period.
Coursework (10%) in the LT.

The coursework will comprise two problem sets during term time.

Key facts

Department: Mathematics

Total students 2021/22: 6

Average class size 2021/22: 6

Capped 2021/22: No

Lecture capture used 2021/22: Yes (LT)

Value: Half Unit

Guidelines for interpreting course guide information

Course selection videos

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

Personal development skills

  • Self-management
  • Problem solving
  • Application of information skills
  • Application of numeracy skills
  • Specialist skills