## Mila Optimization Crash Course

## Goal

The goal of this crash course is to present standard proof techniques for simple optimization algorithms.

It is tailored for practitioners who use optimization as black box tools, e.g., SGD or ADAM to optimize neural networks and want to understand the underlying principles of optimization.

The overall idea is to present each building block of the ADAM optimizer.

For each lecture, proofs will be done onboard and at least 30 minutes will be dedicated to redo the proofs by yourself. Lecture notes will be released on the fly.

## When & Where

Wednesday 15h-17h, room H04 (Mila 6650 building).

## Organizers

Danilo Vucetic, Lucas Maes, Damien Scieur and Quentin Bertrand

## Attempted Schedule

The first sessions, from basic concepts to stochastic gradient descent, will be lecture-based, and the last ones will be seminar-based sessions.

02-14-2024 Basic concepts, convexity, smoothness, convergence proof of gradient descent (Lecturer: Quentin Bertrand)

References: Lecture notes from Sham Kakade, Ryan Tibshirani, Ioannis Mitliagkas, Robert Gower, Mathurin Massias (Chapters 2 and 3). You can also check Yuri Nesterov's book (Chapters 1 and 2)

02-21-2024 Subgradient Descent and Dual averaging (Lecturer: Damien Scieur)

References: Lectures notes from Jiantao Jiao

02-28-2024 Convergence proof of gradient and subgradient descent Part 2 (Lecturer: Quentin Bertrand)

03-06-2024 Acceleration: Nesterov and heavy ball (Lecturer: Damien Scieur)

References: Chapter 4 of Damien's monograph

03-13-2024 Stochastic gradient descent (Lecturer: Quentin Bertrand)

References: Fabian Pedregosa blog posts for intuitions and proofs, Lieven Vandenberghe Lecture's notes, Simon Lacoste-Julien Lecture notes on stochastic subgradient method and convex optimization, Guillaume Garrigos and Robert Gower monography

03-20-2024 Adaptive methods: line search and Polyak step size (Lecturer: Damien Scieur)

03-27-2024 RMSProp and ADAM (Lecturer: Charles Guille-Escuret)

04-17-2024 Automated proof techniques (Lecturer: Gauthier Gidel)

04-24-2024 New adaptive techniques for deep learning (Lecturer: Damien Scieur)