Prof Laszlo Vegh COL 2.02

This course is available on the BSc in Business Mathematics and Statistics, 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 have a knowledge of continuous optimisation to the level of 'Optimisation Theory (MA208)'.

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. First-order methods and convergence guarantees, including conditional gradient descent, stochastic gradient descent. Online convex optimization, online gradient and multiplicative weight methods. Second-order optimization, Newton’s method, quasi-Newton methods. Interior-point methods. Quadratic programming, support vector machines. Fundamental concepts in neural networks. Reinforcement learning, multi-armed bandit problems.

This course is delivered through a combination of classes and lectures totalling a minimum of 32 hours across Lent and Summer term. This year, apart from pre-recorded lecture videos, there will be a weekly live online session of an hour. Depending on circumstances, classes might be online.

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

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

• Boyd, S., & Vandenberghe, L. (2004). Convex optimization. Cambridge University Press.
• Shalev-Shwartz, S. & Ben-David, S. (2004). Understanding Machine Learning: From Theory to Algorithms. . Cambridge University Press.
• Nesterov, Y. (2018). Lectures on convex optimization (Vol. 137). Springer.
• Blum, A., Hopcroft, J., & Kannan, R. (2020). Foundations of data science. Cambridge University Press.
• Vishnoi, N. (2018). Algorithms for Convex Optimization (2021). Cambridge University Press.

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.

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