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261-5110-00L 10 Credits MSC , WBZ D-ITET , D-INFK , D-MATH
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Optimization for Data Science

Lecturers & Examiners: Prof. Dr. Bernd Gärtner, Prof. Dr. David Steurer, Prof. Dr. Niao He
VVZ CR 1.7

Last Updated: 2026-02-05 15:55:03

Abstract

This course provides an in-depth theoretical treatment of optimization methods that are particularly relevant in data science.

Objective

Understanding the theoretical guarantees (and their limits) of relevant optimization methods used in data science. Learning general paradigms to deal with optimization problems arising in data science.

Content

This course provides an in-depth theoretical treatment of optimization methods that are particularly relevant in machine learning and data science. In the first part of the course, we will first give a brief introduction to convex optimization, with some basic motivating examples from machine learning. Then we will analyse classical and more recent first and second order methods for convex optimization: gradient descent, Nesterov's accelerated method, proximal and splitting algorithms, subgradient descent, stochastic gradient descent, variance-reduced methods, Newton's method, and Quasi-Newton methods. The emphasis will be on analysis techniques that occur repeatedly in convergence analyses for various classes of convex functions. We will also discuss some classical and recent theoretical results for nonconvex optimization. In the second part, we discuss convex programming relaxations as a powerful and versatile paradigm for designing efficient algorithms to solve computational problems arising in data science. We will learn about this paradigm and develop a unified perspective on it through the lens of the sum-of-squares semidefinite programming hierarchy. As applications, we are discussing non-negative matrix factorization, compressed sensing and sparse linear regression, matrix completion and phase retrieval, as well as robust estimation.

Resources

Learning Materials (Links)

General Information

Language
English
Levels
MSC , WBZ
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 180 minutes
Aids
None
At two times in the course of the semester, we will hand out specially marked exercises or term projects (compulsory continuous performance assessments) - the written part of the solutions are expected to be typeset in LaTeX or similar. Solutions will be graded, and the grades will account for 20% of the final grade. Assignments can be discussed with colleagues, but we expect an independent writeup.

Course Components

Type Title Time & Place Hours
lecture Optimization for Data Science
  • Mon 13:15-14:00 (NO C 60)
  • Tue 10:15-12:00 (ETF C 1)
3 h weekly
exercise Optimization for Data Science
  • Tue 14:15-16:00 (HG D 5.2)
  • Tue 14:15-16:00 (ML H 44)
2 h weekly
independent project Optimization for Data Science No time listed 4 h weekly

Offered In