Teaching - Mathematical Algorithmic Optimization

Lecture: Optimization Methods for Machine Learning

News

All inverted classrooms take place virtually until further notice. You can pose questions in our MatterMost group at any time.

The lecture (LSF) will be taught in English and addresses Master and PhD students in Mathematics or related fields. We will use a hybrid format, with videos of the lectures that can be asynchronically assessed and on-site inverted classroom lectures and practical exercises.

Exercises and Downloads

The main resource of videos, pdfs, and exercise material is this website that you can access with a password provided in the lecture. The following table specifies when we are going to talk about which contents (i.e., until when you should have studied which material).

Date	Chapter	Chapter Name	File name
11.10.22, 11h15	0	Organizational stuff	organization
18.10.22, 11h15	1.1	History of AI and ML	omml_1.1
18.10.22, 11h15	1.2	Some Concepts	omml_1.2
1.11.22, 11h15	2.1	Case Study: Text Classification	omml_2.1a, omml_2.1b
1.11.22, 11h15	2.2	Case Study: Image Recognition	omml_2.2
8.11.22, 11h15	2.3	Universal approximation theorem	omml_2.3
8.11.22, 11h15	2.4	Incorporating Domain Knowledge	omml_2.4
15.11.22, 11h15	3.1	Overview: Optimization Problem	omml_3.1
22.11.22, 11h15	3.2	Overview: Methods	omml_3.2a, omml_3.2b
29.11.22, 11h15	4.1	Derivatives for general functions F	omml_4.1
6.12.22, 11h15	4.2	Backpropagation as a Special Case of AD	omml_4.2
6.12.22, 11h15	4.3	Deep Learning and Differential Equations	omml_4.3
13.12.22, 11h15	5.1-2	Preliminaries, First Convergence Results	omml_5.1-2
10.1.23, 11h15	5.3	Convergence Results for Strong Convexity	omml_5.3
10.1.23, 11h15	5.4-5.5	Convergence Results for General Objectives, Work Complexity	omml_5.4
17.1.23, 11h15	6	Noise Reduction Methods	omml_6
17.1.23, 11h15	7	Second-Order Methods	omml_7
24.1.23, 11h15	8.1	Gradient Methods with Momentum	8.1_gradientmomentum (no video)
24.1.23, 11h15	8.2	Gradient Methods with Acceleration	8.2_acceleratedgradient (no video)
24.1.23, 11h15	8.3	Alternating Direction Methods	8.3_admm (no video)

18.10.22, 11h15	9.01	AI and the Work Market	omml_9.01
1.11.22, 11h15	9.02	AI and the Work Market 2	omml_9.02
1.11.22, 11h15	9.03	AI and Creativity	omml_9.03
8.11.22, 11h15	9.04	How the Enlightenment ends	omml_9.04
15.11.22, 11h15	9.05	AI and Consciousness	omml_9.05
22.11.22, 11h15	9.06	Why are Myths so important?	omml_9.06
29.11.22, 11h15	9.07	AI and TÜV	omml_9.07
6.12.22, 11h15	9.08	Algorithms and Humanism	omml_9.08
13.12.22, 11h15	9.09	AI and Dataism	omml_9.09
20.12.22, 11h15	9.10	AI and The Matrix	omml_9.10
10.1.23, 11h15	9.11	AI and Research	omml_9.11
17.1.23, 11h15	9.12	Evolution and Intelligent Design	omml_9.12
24.1.23, 11h15	9.13	AI, Economy, and Politics	omml_9.13
24.1.23, 11h15	9.14	AI, Social Scoring, and Fairness	omml_9.14

The pdf slides may be updated and extended during the course of the semester. The complete material in one file omml.pdf will be made available as one complete pdf, also in a printable 4-on-1 format at the end of the course.

Information

Lecture with 4+2 SWS and 9 ECTS-Credits
Inverted classroom on Tue 11h15-12h45 (G05-211) and exercises on Fri 13h15-14h45 (G05-117). The time slot on Wed 7h15-8h45 is reserved for looking at the asynchronous lecture material.
Lecturer practical exercises and

Requirements

Mathematical basics (Analysis and Linear Algebra) and programming skills. Introduction to Optimization. The lecture Nonlinear Optimization is highly recommended, but not absolutely necessary.

Module description

The lecture is a master lecture in the mathematics curriculum and described in the module handbook (currently page 31) as a Wahlpflicht module:

WPF MA (Module 12, 13, 14)
WPF MA;M 1-3 (Module M3D)

A translation of the module description:

Goals and competences: The students acquire competences with respect to modeling and algorithmically solving optimization problems that are at the basis of modern machine learning techniques. A rigorous mathematical analysis of convergence theory and implementation aspects of different algorithms is the guiding theme of the lecture. In the exercises the students learn how to implement algorithms efficiently on a computer and to apply them to concrete problem instances.
Content: An introduction to mathematically formulating machine learning problems in a generalized way, calculating derivatives, stochastic and deterministic derivative-based algorithms, convergence theory. See above for a table of contents.

The lecture is also open to other master and PhD students of OVGU. In particular, there is an agreement that ORBA students may choose the lecture as a Wahlpflicht (with 10 CP to motivate the independent study of mathematical foundations necessary to follow the lecture). However, please note that the lecture is addressed to mathematical master students and assumes a good understanding of mathematical basics, especially in the second part of the lecture. If you are mainly interested in applying machine learning and not so much in analyzing the training process, other lectures might be better suited for you. Note that the lecture Concepts and Algorithms of Optimization is not sufficient as a requirement, you will have to invest more time to acquire additional mathematical knowledge.