Optimization for Machine Learning

Dr. Bogdan Savchynskyy, WiSe 2022/23


This lecture belongs to the Master in Physics (specialization Computational Physics, code "MVSpec"), Master of Applied Informatics (code "IOML") as well as Master Mathematics programs, but is also open for students of Scientific Computing and anyone interested.

The course presents various existing optimization techniques for such important machine learning tasks, as inference and learning for graphical models in combination with neural networks. In particular, it addresses such topics as combinatorial algorithms, integer linear programs, scalable convex and non-convex optimization, convex duality theory, learning of combinatorial algorithms with neural networks. Graphical models play a role of a working example along the course. The goal of the course is to give a strong background for analysis of existing, and development of new scalable optimization techniques for machine learning problems.

Schedule and Information

The lectures and exercises will be given in English .

Lecture schedule:

  • Lecture: Mo, 11:00 – 13:00,
  • Lecture: Wed, 14:00 – 16:00, the first lecture will be given on October 19
  • Exercises: Wed, 16:00 – 18:00, the first exercise will take place on October 26

Contact for questions: Dr. Bogdan Savchynskyy

The seminar Optimization in Machine Learning and Computer Vision complements this lecture by taking a closer look at recent results and developments. We highly recommend it to all students interested in the topic.


Please register for the course in Müsli. The link to join the lecture will be send via email to the registered students only.

Course Material and Exercises


Table of Contents

I Inference in Graphical Models

  • Acyclic Graphical Models. Dynamic Programming
  • Background: Basics of Linear Programs and Their Geometry
  • Inference in Graphical Models as Integer Linear Program
  • Background: Basics of Convex Analysis and Convex Duality
  • Duality of the LP Relaxation of Inference Problem
  • Background: Basics of Convex Optimization
  • Sub-Gradient and Block-Coordinate Ascent for Inference in Graphical Models
  • Lagrangian (Dual) Decomposition
  • Min-Cut/Max-Flow Based Inference
  • LP Relaxation of Inference Problem as st-Min-Cut Problem
  • Summary: Inference Algorithm Selection

II Joint Learning of Graphical Models and Neural Networks

  • Learning of Combinatorial Algorithms: General Concepts and Definitions.
  • Learning of Combinatorial Algorithms with Neural Networks: Structured Risk Minimization.
  • Learning of Combinatorial Algorithms with Neural Networks: Black-Box Differentiation.