Seminar: Machine Learning and Optimization

Previous Seminars:

Winter 2024/2025: Elements of Causal Inference

Based on the book "Elements of Causal Inference" by Jonas Peters, Dominik Janzing and Bernhard Schölkopf, 2017 (link)

We are excited to announce an upcoming seminar that delves into the emerging fusion of modern statistical inference, commonly known as machine learning (ML) or artificial intelligence (AI), and causal inference methods. This seminar is based on the insights from a pioneering book that offers a comprehensive introduction to this interdisciplinary field.

Seminar Overview:

• Introduction to Predictive and Causal Inference: We will begin with an overview of key concepts in both predictive and causal inference. Predictive inference focuses on prediction and description without requiring causal interpretation, while causal inference aims to uncover the underlying cause-effect relationships.

• Popular ML/AI Methods: Participants will receive a high-level introduction to popular machine learning methods such as Lasso, random forests, and deep neural networks. This segment is designed to equip attendees with the necessary background to understand and apply these tools in causal inference contexts.

• Cause-Effect Problem: The seminar will delve into the cause-effect problem within systems containing only two observables. This discussion will provide a foundation for understanding more complex causal structures.

• Interplay Between ML and Causal Inference: We will explore how methods from machine learning and computational statistics can aid in the inference of causal structures. Moreover, we will discuss how causal reasoning can inform and enhance the practice of machine learning.

This seminar requires a solid mathematical concepts related to probability, statistics and machine learning.

We will roughly cover the following topics:

• Statistical and Causal Models

• Assumptions for Causal Inference

• Cause-Effect Models

• Learning Cause-Effect Models

• Connections to Machine Learning - Part 1

• Multivariate Causal Models

• Learning Multivariate Causal Models

• Connections to Machine Learning - Part 2

• Hidden Variables

• Time Series

This seminar will be based on the following book:

"Elements of Causal Inference", Jonas Peters, Dominik Janzing and Bernhard Schölkopf, 2017 (link)

Prerequisites

• Calculus and linear algebra: Familiarity with basic matrix manipulations and concepts from calculus (e.g., differentiability, gradient, continuity)

• Pleasure with mathematically rigorous statements: Sufficient mathematical maturity regarding proof techniques (direct proof, proof by contradiction, composition)

• Basic knowledge on probability: Familiarity with the following concepts: event, random variable, probability density function, cumulative distribution function, conditional probability, independence, expected value, variance, etc.

Logistics

• Seminar: Mondays 15:15 - 16:45, room P602

• Grade: Based on your presentation and prepared report (6-8 pages)

• Template for report

Schedule 

• Monday 21.10: Statistical and Causal Models (book chapter 1) - Tobias Sutter & distribution of topics

• Monday 28.10: Assumptions for Causal Inference (book chapter 2) - Tobias Sutter

• Monday 4.11: Self study preparation time

• Monday 11.11 Cause-Effect Models (book chapter 3) - Paula Tauber

• Monday 18.11: Self study preparation time

• Monday 25.11: Learning Cause-Effect Models (book chapter 4) - Lucas Von Mullen Brown

• Monday 2.12: No Seminar

• Monday 9.12: Connections to Machine Learning - Part 1 (book chapter 5) - Dafina Kastrati

• Monday 16.12: Multivariate Causal Models (book chapter 6) - part 1 by Fabian Zorr and part 2 by Johannes Aumann

• Christmas break

• Monday 13.1: Connections to Machine Learning - Part 2 (chapter 8) - Lia Froitzheim

• Monday 20.1: Hidden Variables (chapter 9) - Tino Zalac

• Monday 27.1: Time Series (chapter 10) - Anna Puchkina & Active Bayesian Causal Inference - Abdelrahman Abdelnaby 

• Monday 3.2: Special Guest: Lecture by Prof. Jana Marekova

Summer 2024: Introduction to Online Nonstochastic Control

 Based on the book "Introduction to Online Nonstochastic Control", Elad Hazan, 2022 (link)

Control theory is the engineering science of manipulating physical systems to achieve desired functionality. Its history is centuries old, and it spans rich areas from the mathematical sciences. A brief list includes differential equations, operator theory and linear algebra, functional analysis, harmonic analysis, and more. However, it mostly does not concern modern algorithmic theory and computational complexity from computer science. The advance of the deep learning revolution has brought to light the power and robustness of algorithms that are based on gradient methods.

This Seminar concerns this exact observation: how can we exploit the differentiable structure in natural physical environments to create efficient and robust gradient-based algorithms for control?

The answer we give is not to apply gradient descent to any existing algorithm. Rather, we rethink the paradigm of control from the start. What can be achieved in a given dynamical system, whether known or unknown, fully observed or not, linear or non-linear, and without assumptions on the noise sequence? This is a deep and difficult question that we fall short of answering. We do, however, propose a different way of answering this question: we define the control problem from the point of view of an online player in a repeated game. This gives rise to a simple but powerful framework called nonstochastic control theory. The framework is a natural fit to apply techniques from online convex optimization, resulting in new, efficient, gradient based control methods.

This seminar will provide an introduction to the concept or Online Nonstochastic Control, which requires a solid mathematical concepts related to convex optimization and Markov decision processes.

We will roughly cover the following topics:

• Dynamical systems

• Markov Decision Processes

• Linear Dynamical Systems

• Optimal Control of Linear Dynamical Systems

• Policy classes for dynamical systems

• Online Nonstochatic Control

• Policy Classes for Partially Observed LDS

• Online Nonstochastic Control with Partial Observation

• Online Nonstochastic System Identification

• Learning in Unknown LDS

• Spectral Filtering

This seminar will be based on the following book:

"Introduction to Online Nonstochastic Control",  Elad Hazan, 2022 (link)

Prerequisites

• Calculus and linear algebra: Familiarity with basic matrix manipulations and concepts from calculus (e.g., differentiability, gradient, continuity)

• Pleasure with mathematically rigorous statements: Sufficient mathematical maturity regarding proof techniques (direct proof, proof by contradiction, composition)

• Basic knowledge on probability: Familiarity with the following concepts: event, random variable, probability density function, cumulative distribution function, conditional probability, independence, expected value, variance, etc.

Logistics

• Seminar: Fridays 10:00 - 11:30, room L829

• Grade: Based on your presentation and prepared report (6-8 pages)

• Template for report

Schedule 

• Friday 12.04: Introduction (book chapter 1) - Tobias Sutter & distribution of topics

• Friday 19.04: Dynamical Systems (book chapter 2) - Tobias Sutter

• Friday 26.04: Self study preparation time

• Friday 03.05 Self study preparation time

• Friday 10.05: Topic 1: Markov Decision Processes (book chapter 3) - Jonas Dickhoefer

• Friday 17.05: Topic 2: Linear Dynamical Systems (book chapter 4) - Pranjal Kandjhari

• Friday 24.05: Topic 3: Optimal Control of Linear Dynamical Systems (book chapter 5) - Jan Reichle

• Friday 31.05: break - no seminar

• Friday 07.06: break - no seminar

• Friday 14.06: Topic 4: Policy Classes for Dynamical Systems (book chapter 6) - Askar Bozcan

• Friday 21.06: break - no seminar

• Friday 28.06: Topic 5: Online Nonstochastic Control (book chapter 7) - Thomas Beha

• Friday 05.07: Topic 6: Policy Classes for Partially Observed LDS and Online Nonstochastic Control with Partial Observation (book chapters 8 & 9) - Tobias Sutter

• Friday 12.07: Topic 7: System Identification (book chapter 10) - Tobias Sutter

Topic for Summer 2023: Introduction to Online  Convex Optimization

Based on Introduction to Online Convex Optimization, Elad Hazan, 2021 (link)

Online Convex Optimization (OCO) considers optimization as a process. In many practical applications, the environment is so complex that it is not feasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary, as well as beneficial, to take a robust approach, by applying an optimization method that learns as more aspects of the problem are observed. This view of optimization as a process has become prominent in various fields, which has led to spectacular successes in modeling and systems that are now part of our daily lives.

The growing body of literature of machine learning, statistics, decision science, and mathematical optimization blurs the classical distinctions between deterministic modeling, stochastic modeling, and optimization methodology. This seminar continues this trend by studying a prominent optimization framework whose precise location in the mathematical sciences is unclear: the framework of online convex optimization (OCO), which was first defined in the machine learning literature. The metric of success is borrowed from game theory, and the framework is closely tied to statistical learning theory and convex optimization.

This seminar will provide an introduction to the concept or Online Convex Optimization, which requires a solid mathematical concepts related to convex optimization and Markov decision processes.

We will roughly cover the following topics:

• Basic concepts in convex optimization (provided by myself during the first two weeks)

• First order algorithms for online convex optimization

• Second order methods

• Regularization

• Bandit convex optimization

• Projection-free algorithms

• Games, duality and regret

• Learning theory, generalization and online convex optimization

• Learning in changing environments

• Boosting and regret

This seminar will be based on the following book:

1) Introduction to Online Convex Optimization, Elad Hazan, 2021 (link)

Prerequisites

• Calculus and linear algebra: Familiarity with basic matrix manipulations and concepts from calculus (e.g., differentiability, gradient, continuity)

• Pleasure with mathematically rigorous statements: Sufficient mathematical maturity regarding proof techniques (direct proof, proof by contradiction, composition)

• Basic knowledge on probability: Familiarity with the following concepts: event, random variable, probability density function, cumulative distribution function, conditional probability, independence, expected value, variance, etc.

Logistics

• Seminar: Fridays 10:00 - 11:30, room P601

• Grade: Based on your presentation and prepared report (5-8 pages)

• Template for report

Schedule 

• Friday 14.04:  Introduction (book chapter 1) - Tobias Sutter & distribution of topics

• Friday 21.04: Basic concepts of convex optimization (book chapter 2) - Tobias Sutter

• Friday 28.04: Self study preparation time

• Friday 05.05 Topic 1: First order algorithms for online convex optimization (book chapter 3) - Tobias Sutter

• Friday 12.05: Topic 2: Second order methods (book chapter 4) - Tobias Sutter

• Friday 19.05: Topic 3: Regularization (book chapter 5) - Tobias Sutter

• Friday 26.05: Topic 4: Bandit convex optimization (chapter 6) - Eva Isakeit

• Friday 02.06: break - no seminar

• Friday 09.06: Holidays

• Friday 16.06: Topic 5: Projection-free algorithms (chapter 7) - Annika Treutle

• Friday 23.06: Topic 6: Games, duality and regret (chapter 8) - Daniel Schwarzkopf

• Friday 30.06:  Topic 7: Learning theory, generalization and online convex optimization (chapter 9) - Christopher Ries

• Friday 07.07: Topic 8: Learning in changing environments (chapter 10) - Manuel Schmidt

• Friday 14.07 Topic 9: Boosting and regret (chapter 11) - Tobias Sutter

• Friday 21.07: Special guest lecture - tbd

Schedule

• Friday 15.4: No seminar (Good Friday)

• Friday 22.4: Self study read Chapter 1 (Introduction) of the fairness book (p. 9 - p. 32)

• Friday 29.4: Frist Seminar event - lecture provided by Tobias Sutter & distribution of topics

• Friday 6.5 Lecture by Tobias Sutter on classification (report)

• Friday 13.5: Self study preparation time

• Friday 20.5: Self study preparation time

• Friday 27.5: Causality 1 (p.77 - 97) by Andreas Kahabka (report)

• Friday 3.6: Causality 2 (p.97-119) by Julian Bauer (report)

• Friday 10.6: Part 1: Traditional tests for discrimination (p.119-136) by Jonas Bachmann (report)

• Friday 17.6: Break 

• Friday 24.6: Part 2: Testing discrimination in algorithmic settings (p.136-154) by Jan de Boer (report)

• Friday 1.7: A broader view on discrimination (p.157-187) by Theodor Gutschlag (report)

• Friday 8.7: Self study - Datasets (p.187-219)

• Friday 15.7 Special guest lecture by Felix Petersen 

• Friday 22.7: Advanced topics (reading material to be provided) by David Boetius (report)