OVERVIEW

The course will illustrate the basic tools needed to understand and use the main optimization and operationa research  algorithms, relevant to solve machine learning and inverse problems.

AIMS AND CONTENT

LEARNING OUTCOMES

The goal of the course is to provide tools for a theoretical understanding and a practical usege of linear programming and  the main convex optimization algorithms used in machine learning and inverse problems. 

AIMS AND LEARNING OUTCOMES

At the end of the course the students will have a working knowledge of convex optimzation and linear programming. In particular, to provide skills to: Recognize convex problems,  understand and use convex optimization algorithms, solve convex problems in real scenarios.

PREREQUISITES

Calculus for functions of several variables, linear algebra, probability

TEACHING METHODS

Classes on the blackboard and labs

SYLLABUS/CONTENT

The course will cover the basic notions for optimization problems. It will cover the linear programming problem, and optimization algorithms for the minimization of smooth and nonsmooth convex functions. The course will discuss the convergence  properties of gradient descent, stochastic gradient descent and proximal gradient descent. Applications to machine learning and imaging problems will be implemented and used  during the lab sessions. 

RECOMMENDED READING/BIBLIOGRAPHY

S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004

S. Bubeck, Convex Optimization: Algorithms and Complexity, https://arxiv.org/abs/1405.4980?context=cs

S. Salzo, S. Villa, Proximal Gradient Methods for Machine Learning and Imaging, 2022

TEACHERS AND EXAM BOARD

Exam Board

SILVIA VILLA (President)

ERNESTO DE VITO

CESARE MOLINARI (Substitute)

LESSONS

LESSONS START

According to the academic calendar

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

To pass the exam the student have to present a short report. The student can choose one among the following options:

1. analyze and discuss a research article on themse close to the ones studied during classes
2. implement an algorithms presented during the classes (in some programming language)
3. use some available code to analyze synthetic and/or real datasets and discuss the obtained results.

ASSESSMENT METHODS

The report preparation and its discussion are aimed at verifying the student's achievement of an independent critical reasoning capability  in the context of machine learning.

During the report presentation, basic questions d on the topics covered by the course amy be asked.