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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.

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. 

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

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

• 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.