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• Syllabus

Official Course Syllabus

General Information

Elective for: D5-mai, E4, F5, F5-r, F5-mai, I4-fir, M4, Pi5-ssr, MMSR2
Language of instruction: The course will be given in English

Aim

Learning from data is becoming increasingly important in many different engineering fields. Models for learning often rely heavily on optimization; training a machine is often equivalent solving a specific optimization problem. These problems are typically of large-scale. In this course, we will learn how to solve such problems efficiently. The large-scale nature of the problems renders traditional methods inapplicable. We will provide a unified view of algorithms for large-scale convex optimization and treat algorithms for the nonconvex problem of training deep neural networks.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

• know basic convex analysis
• understand the connection between machine learning and optimization
• have an understanding on the role of regularization in learning from an optimization point of view
• understand unifying framework for large-scale convex optimization
• understand concepts such as nonexpansiveness, and averagedness and their relation to monotone operators and their role for convergence of algorithms
• understand how to derive specific algorithms from the few general ones
• understand methods for avoiding numerical issues in deep neural network training.

Competences and skills
For a passing grade the student must

• be able to describe optimality conditions that are useful for large-scale methods
• be able to describe the building blocks that are the foundations of large-scale optimization algorithms and why they are used
• be able to analyze performance of optimization algorithms
• be able to solve optimization problems numerically using software and own implementations
• be able to present results in writing.

Judgement and approach
For a passing grade the student must

• understand what algorithm that should be used for different machine learning training problems
• be able to participate in the team-work needed to solve the hand-in assignments.

Contents

The course has lectures, exercises, and four hand-in assigments.

The lectures will cover:

convexity, models for learning, unified convex optimization algorithm view, fixed-point iterations, monotone operators, nonexpansive mappings, stochastic methods, reduced variance methods, block-coordinate methods, nonconvex stochastic gradient descent and variations for for deep learning training.

Examination details

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Written exam (5 hours), 3 hand-in exercises. In case of less than 5 registered students, the exam may be given in oral form.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Parts
Code: 0121. Name: Exam. 
Credits: 7,5. Grading scale: TH. 
Code: 0221. Name: Hand-in 1. 
Credits: 0. Grading scale: UG. 
Code: 0321. Name: Hand-in 2. 
Credits: 0. Grading scale: UG. 
Code: 0421. Name: Hand-in 3. 
Credits: 0. Grading scale: UG. 

Admission

Assumed prior knowledge: FMAN61 Optimization
The number of participants is limited to: 90
Selection: Completed university credits within the programme. Priority is given to students enrolled on programmes that include the course in their curriculum.

Reading list

• Lecture slides and notes.

Contact and other information

Course coordinator: Pontus Giselsson, pontusg@control.lth.se