## Second year

In this page you will find the description of the different second-year trainings offered within the Master ACSYON.

## The three trainings of the second year of the Master Acsyon

Click on the boxes above to discover the corresponding training :

##### Local M2

This training is dedicated to **english-speaker** students willing to pursue their academic training at the University of Limoges. All courses are given in english and at the University of Limoges.

##### EUR M2

This training is dedicated to **english-speaker** students. It is a variant of the local training, with a special option related to the TACTIC Graduate School. It is the natural follow-up of the EUR M1 training. All courses are given in english at the University of Limoges.

##### MIX M2

This training is dedicated to **french- **and **english-speaker **students. It is the follow-up of the MIX M1 training. This training is addressed to students of the mechatronic training of ENSIL-ENSCI in Limoges. Three courses are delivered in english at the University of Limoges ; the rest of the training is ensured by ENSIL-ENSCI in Limoges, within the mechatronic training.

## List of courses offered by M2 ACSYON

## Description of the courses of the third semester

##### Optimization for large-scale machine learning

**Prérequis**

Optimization basics, linear algebra, convex geometry

**Mots clés**

Large-scale nonlinear optimization, big data optimization

##### Deep learning

**Prérequis**

Basics on numerical linear algebra, differential calculus and machine learning basics, Python

**Mots clés**

Neural network, algorithm, supervised learning, unsupervised learning, gradient descent

##### Applied multilinear algebra

**Prérequis**

Linear algebra, numerical matrix analysis, normed vector space, bilinear algebra, Euclidean spaces, differential calculus in R^n

**Mots clés
**Tensors, rank of tensors, singular value decomposition (HOSVD), tensor compression algorithm

** **

##### Splitting methods for convex optimization

Several practical works (on Matlab or Pyhton) are performed during the semester in order to solve some standard problems that can be found in machine learning and data science, such as LASSO, consensus optimization, matrix decomposition problem, risk-averse optimization, clustering, image restoring (denoising, deblurring, inpainting), etc.

**Prérequis**

Convex analysis, topology, differential calculus, linear algebra and optimization basics

**Mots clés
**Maximal monotone set-values maps and resolvents, firmly non expansive and averaged operators, fixed-point algorithm, Krasnoselskii-Mann algorithm, projection operator, proximal operator, proximal point algorithm, proximal gradient algorithm (forward-backward), Douglas-Rachford algorithm, Davis-Yin algorithm, Lagrangian duality, primal-dual algorithms, method of multipliers, ADMM

** **

##### Fast algorithmic methods for optimization and learning

The second part of this course will be devoted to the link between continuous differential equations and algorithms in optimization (obtained by explicit/implicit temporal discretization). This back and forth between continuous and discrete dynamics allowed us to propose efficient and fast algorithms in optimization. This include:

– damped inertial gradient method for understanding and extending Nesterov accelerated gradient method

– Hessian-driven damping for speeding up and damping oscillations of optimization algorithms,

– Fast algorithms in convex optimization based on inertial gradient-based dynamics

– Asymptotic vanishing damping and its link with Nesterov acceleration.

Applications will be given in image processing such as image denoising, image deconvolution, image inpainting, motion estimation and image segmentation.

**Prérequis**

Linear algebra, topology and differential calculus in R^n, convex analysis, optimization basics

**Mots clés**

First order optimization algorithms, ISTA, FISTA, Nesterov acceleration, damped inertial gradient methods, Hessian-driven damping algorithms, asymptotic vanishing damping

##### Reinforcement learning and stochastic optimization

**Prérequis**

Optimization basics, practical optimization and stochastic processes

##### Online optimization, learning and games

**Mots clés**

Game theory, learning, optimization, gradient-based techniques

##### Miniconferences

**Mots clés
**Thematic conferences, practical cases, applied sciences, business