Master ACSYON - parcours Applied Mathematics & Optimization

Credits: 3
Language:

French

Course mode:

On-site

Methods of delivery:

Lectures (12h)
Tutorials (18h)

Pre-requisites:

Linear algebra, Matrix numerical analysis, Normed vector spaces, Bilinear algebra, Euclidean vector spaces, Differential calculus in R^n.

Objectives:

The aim of this course is to provide an overview of important concepts and algorithms of applied linear algebra, their analysis and some of their applications.

Learning outcomes:

in progress

Indicative contents:

in progress

Methods of assessment:

Written test, practical work

Suggested bibliography:

in progress

Credits: 3
Language:

French

Course mode:

On-site

Methods of delivery:

Lectures (9h)
Tutorials (9h)
Practicals (12h)

Pre-requisites:

Basic notions of algorithms.

Objectives:

This course offers a solid foundation on the different artificial intelligence methods applied in areas as varied as problem solving in large search spaces, the resolution of constraint satisfaction systems or uncertain reasoning.

This module will allow students to master these various AI methods and algorithms and will be able to put them into practice in real situations that they will work on during the Practical Work sessions.

Learning outcomes:

in progress

Indicative contents:

• Search methods with heuristics in a state space;
• Constraint satisfaction problems (CSP);
• Algorithms for games;
• Knowledge representation and expert systems;
• Learning techniques;
• Introduction to neural networks.

Methods of assessment:

Written test, practical work

Suggested bibliography:

• Artificial intelligence Stuart Russell and Peter Norvig Edition Perason, (2010)
• Mooc (on Youtube): Artificial Intelligence course by Hugo Larochelle (Quebec Canada): https://www.youtube.com/watchv=stuU2TK3t0Q&list=PL6Xpj9I5qXYGhsvMWM53ZLfwUInzvYWsm

Credits: 3
Language:

French

Course mode:

On-site

Methods of delivery:

Lectures (12h)
Tutorials (18h)

Pre-requisites:

Normed vector spaces and topology bases.

Objectives:

At the end of the first year of the ACSYON Master, the objective is for the student to perfectly master the basic tools and results of convex analysis, with the aim in particular of facing, in good conditions, the problems of convex optimization encountered during the second year of the ACSYON Master, in particular in the module entitled « Splitting methods for convex optimization ».

Learning outcomes:

in progress

Indicative contents:

This course is an introduction to convex analysis in finite dimensions. The first part of this course focuses on the geometric and topological aspects of convex sets, introducing in particular some very classic theorems (projection theorem, separation theorem, etc.) and their applications (bipolar theorem, Farkas theorem, theorem of Minkowski, etc.). The second part of this course is devoted to the analysis of convex functions, in particular to their regularities (continuity, differentiability, sub-differentiability), and to the notion of Legendre-Fenchel conjugate function.

Methods of assessment:

Written test, practical work

Suggested bibliography:

in progress

Credits: 3
Language:

French

Course mode:

On-site

Methods of delivery:

Lectures (12h)
Tutorials (9h)
Practicals (9h)

Pre-requisites:

Linear algebra, topology and differential calculus in R^n, probability and statistics.

Objectives:

Machine learning is one of the key areas of artificial intelligence and is used in many recent technologies such as: search engines, image recognition, speech recognition, social networks, autonomous vehicles, medical diagnosis etc ….

It concerns the study and development of quantitative models that allow a computer to perform tasks and learn from experience. This course is an introduction to the fundamental concepts and algorithms of machine learning. The main focus of the course is on the design of statistical learning models and the optimization algorithms that are used to train them.

Learning outcomes:

in progress

Indicative contents:

in progress

Methods of assessment:

Written test, practical work

Suggested bibliography:

in progress
 

Credits: 3
Language:

French

Course mode:

On-site

Methods of delivery:

Lectures (12h)
Tutorials (18h)

Pre-requisites:

Linear algebra, differential calculus and topology in finite dimension.

Objectives:

This is an introductory course to optimization theory. We review optimization through history, the different optimization problems: linear vs. nonlinear, continuous vs. discontinuous, unconstrained vs. constrained, global vs. local, convex vs. nonconvex, deterministic vs. stochastic. We demonstrate the KKT (Karush-Khun-Tucker) optimality conditions. We study duality (strong and weak duality), the relationship between the problem and the dual, complementarity problems, sensitivity analysis.

Learning outcomes:

in progress

Indicative contents:

This course is an introduction to convex analysis in finite dimensions. The first part of this course focuses on the geometric and topological aspects of convex sets, introducing in particular some very classic theorems (projection theorem, separation theorem, etc.) and their applications (bipolar theorem, Farkas theorem, theorem of Minkowski, etc.). The second part of this course is devoted to the analysis of convex functions, in particular to their regularities (continuity, differentiability, sub-differentiability), and to the notion of Legendre-Fenchel conjugate function.

Methods of assessment:

Written test

Suggested bibliography:

in progress

Credits: 3
Language:

French

Course mode:

On-site

Methods of delivery:

Lectures (12h)

Tutorials (9h)

Practices (9h)

Pre-requisites:

Basic numerical linear algebra and differential calculus. The software OCTAVE will be used for the numerical computations. Note that MATLAB can be equivalently used. Examples and solutions will be given with the OCTAVE/MATLAB syntax. The modeling language AMPL will be installed on your computer during the first week. You will be given a free trial license to install this software.

Objectives:

The goal is to learn how to effectively solve an optimization problem. We will see how to modelize an optimization problem and to compute an optimal solution in some concrete situations. We will basically work on optimality conditions of an optimization problem. We will recall the optimality conditions and how to numerically solve them. Outline of the course: Review on some tools from linear algebra, differential calculus and convexity – Warm-up with Matlab/Octave – Introduction to optimization – Modeling languages – First steps with AMPL – Unconstrained optimization – Least-squares problems – Linear programming- Nonlinear programming.

Learning outcomes:

Learn to solve an optimisation problem numerically.

Indicative contents:

in progress

Methods of assessment:

Written test, practical work

Suggested bibliography:

Fourer, R., Gay, D.M., Kernighan, B.W.: AMPL: A Modeling Language for Mathematical Program- ming, 2nd edn. Brooks/Cole, Pacific Grove (2002)

Credits: 6
Language:

French

Course mode:

On-site

Methods of delivery:

Lectures (30h)

Practices (30h)

Pre-requisites:

in progress

Objectives:

in progress

Learning outcomes:

in progress

Indicative contents:

Analysis and proofs of algorithms, loop invariants. Elementary arithmetic, Euclid’s algorithm, fast exponentiation. Sorting algorithms (insertion, merge, bubbles, quicksort) and analysis of their costs. Boolean algebra, Boolean functions. Graphs (Eulerian paths, Hamiltonian paths, 4-color theorem). Practical work: C programming (types, functions, pointers, makefiles). Development of a project in a small group.

Methods of assessment:

Written test, practical work

Suggested bibliography:

in progress

Credits:3
Language:

French

Course mode:

On-site

Methods of delivery:

Tutorials (39h)

Pre-requisites:

None

Objectives:

Part 1 Communication : This module is designed to help students apply for internships. It equips them with methodological tools and enables them to understand the challenges and stages of recruitment. In addition, students reinforce their oral fluency through a number of exercises: a 180-second Elevator pitch; a critical analysis of a socio-technical controversy in its polemical and media dimensions, combined with a presentation of the players involved and the arguments associated with the different positions. The aim is to develop convincing and adaptable skills. Team-building exercises are designed to get students to work together and put them in a collective interview situation. – Pay attention to posture and body language – Express yourself with ease – Synthesize – Analyze documents and identify arguments – Present a project, justifying the choices made

Part 2 Management : This module aims to make students think about the issues facing a company, how the right strategy is determined, using methodological tools, and to identify interested parties and their performance management.

Learning outcomes:

• Develop your human and relational qualities
• Communicate in writing, orally, in several languages
• Work as a team, self-assess (strengths and weaknesses)
• Develop your abilities to enter professional life
• Demonstrate cultural openness, be curious, have a critical mind
• Work on your dynamism, be capable of commitment, leadership
• Know how to integrate business and societal issues in an international context
• Know and understand the business world
• Manage projects

Indicative contents:

Part 1 Communication : Job interview simulations (individual and collective) are offered as well as the creation of the key elements of a file, namely the CV, cover letter, LinkedIn profile, online applications, etc. A current review (scientific and technical news) is produced at each tutorial as well as a final presentation on a subject related to the professional world. This requires documentary research and preparation of the speech as well as the visual support used for the defense. Work on argumentation and the rhetorical aspects of speech is presented. Students approach a socio-technical controversy by identifying the various positions and issues at stake in the debate, particularly in its media dimension. They report on their documentary research and the choices they have made to address the controversy in an oral presentation.

Part 2 Management :

Chap 1. The company and its environment

• The company
• Analysis of its environment, its market
• The choice of a strategy thanks to a good diagnosis
• React to changes in the environment

Chap 2. The company and its strategic choices

• Notions – strategy, organizational policy, competitive advantage, the different levels of strategy
• The 3 strategies resulting from Porter methods
• Growth strategies * Innovation * Entrepreneurial and managerial logic
• The purpose of a company

Chap 3. Company performance.

• Company management and performance
• Identify stakeholders and their objectives
• Concept- governance, management, performance, decision-makers

Methods of assessment:

Written test, oral, presentation

Suggested bibliography:

• Perez D., CV, lettre de motivation, entretien d’embauche, L’Étudiant, Ed. Paris, 2014, 416 pages.
• Engrand S., Projet professionnel gagnant ! Une méthode innovante pour cibler stages et premier emploi, Dunod, Ed. Paris, 2014, 180 pages.
• Davidenkoff E., Le guide des entreprises qui recrutent : hors-série 2015 : faire la différence en entretien, négocier son premier salaire, débuter à l’étranger, L’Étudiant, Ed. Paris, 2015
• Charline Licette, Savoir parler en public, Studyrama Pro, 2018
• Fabrice Carlier, Réussir ma première prise de parole en public, StudyramaPro, 2018
• Cyril Gely, Savoir improviser : l’art de s’exprimer sans préparation, Groupe Studyrama-Vocatis, 2010
• Lelli A., 2003, Les écrits professionnels : la méthode des 7C – Soyez correct, clair, concis, courtois, convivial, convaincant, compétent, Dunod, Ed. Paris, 2003, 168 pages.

Credits: 6
Language:

French/English

Course mode:

On-site

Pre-requisites:

None

Objectives:

Consolidation of the experience acquired during training within a research laboratory.

Indicative contents:

Depending on the topic of the laboratory work.

Learning outcomes:

• Integrate into and within a work team
• Show initiative
• Test your curiosity
• Structure your ideas and the stages of their implementation
• Demonstrate scientific rigor
• Learn to meet deadlines
• Know the safety rules in force within the structure

Methods of assessment:

Report, evaluation sheet (lab behavior), oral presentation

Suggested bibliography:

Depending on the topic of the laboratory work.

Credits: 3
Language:

French

Course mode:

On-site

Methods of delivery:

Lectures (9h)

Tutorials (9h)

Practices (12h)

Pre-requisites:

Basic notions of algorithms.

Objectives:

The objective of this course is to allow students to master the fundamental concepts of machine learning and to apply these notions to certain concrete problems such as information security. Then to make them acquire knowledge on supervised and unsupervised learning techniques.

Learning outcomes:

At the end of this activity, the student will have acquired knowledge on:

• Allow students to master the fundamental concepts of machine learning and apply these concepts to real-world problems.
• Help them acquire knowledge of supervised and unsupervised learning techniques.
• Indicative contents:
• Expert system generators;
• Genetic algorithms;
• Introduction to Bayesian networks;
• Distributed artificial intelligence: Introduction to multi-agent systems;
• Intelligent systems based on ant colonies

Methods of assessment:

Written test, practical work

Suggested bibliography:

Apprentissage artificiel, concepts et algorithmes, Eyrolles.

Credits: 3
Language:

French

Course mode:

On-site

Methods of delivery:

Lectures (9h)

Tutorials (9h)

Practices (12h)

Pre-requisites:

in progress

Objectives:

Introduction to game theory:

• Solution Concepts
• Games in normal form: dominant/dominated strategies
• Nash equilibrium
• Pareto criterion
• Mixed strategies and zero-sum games
• Extensive form games: correlated equilibria
• Repeated games

Learning outcomes:

in progress

Indicative contents:

This UE is an introduction to game theory and its applications in computer science. It could also be called interactive decision theory, because it models situations in which several agents make choices that in turn have effects on gains (or losses), those of some affecting the gains of others.

Nash equilibrium, non-cooperative games, dominant/dominated strategies.

Methods of assessment:

Written test, practical work

Suggested bibliography:

in progress

Credits: 3
Language:

French

Course mode:

On-site

Methods of delivery:

Lectures (12h)

Tutorials (9h)

Practices (9h)

Pre-requisites:

Elementary linear algebra and convex geometry.

Objectives:

The course consists of an introduction to linear (LP) and quadratic (QP) optimization. We focus on duality aspects in LP, the simplex method for linear programming, optimality and complementarity conditions, and interior point methods. In the second part of the course, we focus on quadratic optimization without constraints and with linear constraints of equality and inequality type, and its resolution. We will cover examples of applications, in particular for data science, decision theory and financial mathematics, for example portfolio optimization, static planning, transportation problems and network design. Practical work will be based on programming with Matlab/Scilab.

Learning outcomes:

in progress

Indicative contents:

Conic optimization, duality, optimality conditions, simplex algorithm, interior point methods, numerical solvers.

Methods of assessment:

Written test, practical work

Suggested bibliography:

in progress

Credits: 3
Language:

English

Course mode:

On-site/Online

Methods of delivery:

Lectures (12h)

Tutorials (9h)

Practices (9h)

Pre-requisites:

• Basic Linear Algebra
• Basic notions of Probability Theory and Statistics
• Notions of Python programming

Objectives:

This course is an introduction to Machine Learning with Python, Scikit-learn and Tensorflow. The objective is to learn to handle Python in order to solve practical problems of machine learning.

• Learn to solve machine learning problems with Python and Scikit-Learn
• Learn to use Tensorflow for Deep Learning applications

Learning outcomes:

Be able solve real life machine-learning problems

Indicative contents:

The course is divided in four parts, on the first part we will learn the basics of Python language and we will also study the package Numpy that allow to manipulate arrays in Python (Arrays are a way to create vector, matrices, tensors). We will also take a look at the Pandas package that is very useful for manipulating data files.

The second part of the course will focus on solving classical machine learning problems using the scikit-learn library. This will enable us to go back over the mathematics used by some of these classic learning methods.

In the third part we’ll learn the basics of Tensorflow to create artificial neural network models for statistical learning, and finally in the fourth part we’ll look at deep learning models and how to train them with Tensorflow.

Methods of assessment:

Written test, practical work with Python

Suggested bibliography:

• Friedman J., Hastie,T. and Tibshirani R. (2001). The Elements of Statistical Learning
• A. Géron (2017), Hands-on Machine Learning with Scikit-Learn & Tensorflow
• C. C. Aggarwal (2018), Neural Networks and Deep Learning

Credits: 3
Language:

French

Course mode:

On-site

Methods of delivery:

Lectures (9h)

Practices (21h)

Pre-requisites:

in progress

Objectives:

in progress

Learning outcomes:

in progress

Indicative contents:

in progress

Methods of assessment:

Written test, project

Suggested bibliography:

in progress
 

Credits: 3
Language:

French

Course mode:

On-site

Methods of delivery:

Lectures (12h)

Tutorials (18h)

Pre-requisites:

None

Objectives:

in progress

Learning outcomes:

in progress

Indicative contents:

in progress

Methods of assessment:

Written test

Suggested bibliography:

in progress

Credits: 3
Language:

English

Course mode:

On-site

Methods of delivery:

Tutorials (30h)

Pre-requisites:

B1 level required.

Objectives:

To bring students towards the European B2/C1 level. The operational and evaluable objectives of this training are:

• Understand most situations that might be encountered at work or while traveling in a region where English is spoken for example
• Develop oral and written language skills
• International English communication

Learning outcomes:

Acquisition of English language skills (objective B2/C1). International, specialty and professional English (CV, cover letters, etc.)

Indicative contents:

• Written and oral comprehension/production work on authentic specialist or general English documents
• Interactive debates on general themes
• Language lab work (pronunciation, listening, repetition, etc.)
• Professional English (writing cover letters, CV, professional interview) academic (summary of documents, emails, sum-ups, etc.)
• Work on specialization and general English vocabulary.
• Presentation of a specialty presentation

Methods of assessment:

Written test, oral

Credits:3
Language:

French

Course mode:

On-site

Methods of delivery:

Tutorials (39h)

Pre-requisites:

None

Objectives:

Part 1 Communication : This module is designed to help students apply for internships. It equips them with methodological tools and enables them to understand the challenges and stages of recruitment. In addition, students reinforce their oral fluency through a number of exercises: a 180-second Elevator pitch; a critical analysis of a socio-technical controversy in its polemical and media dimensions, combined with a presentation of the players involved and the arguments associated with the different positions. The aim is to develop convincing and adaptable skills. Team-building exercises are designed to get students to work together and put them in a collective interview situation. – Pay attention to posture and body language – Express yourself with ease – Synthesize – Analyze documents and identify arguments – Present a project, justifying the choices made

Part 2 Management : This module aims to make students think about the issues facing a company, how the right strategy is determined, using methodological tools, and to identify interested parties and their performance management.

Learning outcomes:

• Develop your human and relational qualities
• Communicate in writing, orally, in several languages
• Work as a team, self-assess (strengths and weaknesses)
• Develop your abilities to enter professional life
• Demonstrate cultural openness, be curious, have a critical mind
• Work on your dynamism, be capable of commitment, leadership
• Know how to integrate business and societal issues in an international context
• Know and understand the business world
• Manage projects

Indicative contents:

Part 1 Communication : Job interview simulations (individual and collective) are offered as well as the creation of the key elements of a file, namely the CV, cover letter, LinkedIn profile, online applications, etc. A current review (scientific and technical news) is produced at each tutorial as well as a final presentation on a subject related to the professional world. This requires documentary research and preparation of the speech as well as the visual support used for the defense. Work on argumentation and the rhetorical aspects of speech is presented. Students approach a socio-technical controversy by identifying the various positions and issues at stake in the debate, particularly in its media dimension. They report on their documentary research and the choices they have made to address the controversy in an oral presentation.

Part 2 Management :

Chap 1. The company and its environment

• The company
• Analysis of its environment, its market
• The choice of a strategy thanks to a good diagnosis
• React to changes in the environment

Chap 2. The company and its strategic choices

• Notions – strategy, organizational policy, competitive advantage, the different levels of strategy
• The 3 strategies resulting from Porter methods
• Growth strategies * Innovation * Entrepreneurial and managerial logic
• The purpose of a company

Chap 3. Company performance.

• Company management and performance
• Identify stakeholders and their objectives
• Concept- governance, management, performance, decision-makers

Methods of assessment:

Written test, oral, presentation

Suggested bibliography:

• Perez D., CV, lettre de motivation, entretien d’embauche, L’Étudiant, Ed. Paris, 2014, 416 pages.
• Engrand S., Projet professionnel gagnant ! Une méthode innovante pour cibler stages et premier emploi, Dunod, Ed. Paris, 2014, 180 pages.
• Davidenkoff E., Le guide des entreprises qui recrutent : hors-série 2015 : faire la différence en entretien, négocier son premier salaire, débuter à l’étranger, L’Étudiant, Ed. Paris, 2015
• Charline Licette, Savoir parler en public, Studyrama Pro, 2018
• Fabrice Carlier, Réussir ma première prise de parole en public, StudyramaPro, 2018
• Cyril Gely, Savoir improviser : l’art de s’exprimer sans préparation, Groupe Studyrama-Vocatis, 2010
• Lelli A., 2003, Les écrits professionnels : la méthode des 7C – Soyez correct, clair, concis, courtois, convivial, convaincant, compétent, Dunod, Ed. Paris, 2003, 168 pages.

Credits: 6
Language:

French/English

Course mode:

On-site

Pre-requisites:

None

Objectives:

Consolidation of the experience acquired during training within a research laboratory.

Indicative contents:

Depending on the topic of the laboratory work.

Learning outcomes:

• Integrate into and within a work team
• Show initiative
• Test your curiosity
• Structure your ideas and the stages of their implementation
• Demonstrate scientific rigor
• Learn to meet deadlines
• Know the safety rules in force within the structure

Methods of assessment:

Report, evaluation sheet (lab behavior), oral presentation

Suggested bibliography:

Depending on the topic of the laboratory work.

Credits: 3
Language:

French/English

Course mode:

On-site (internship)

Pre-requisites:

None

Objectives:

Discover the world of business or international research work.

Learning outcomes:

Compare the skills acquired during training with the demands of the socio-professional world.

Indicative contents:

At least two months spent within the company (or in an international research laboratory) as an intern.

Methods of assessment:

Report, evaluation sheet, oral presentation

Credits: 4
Language:

English

Course mode:

On-site

Methods of delivery:

Lectures (12h)

Tutorials (18h)

Pre-requisites:

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

Objectives:

This course is a continuation of the M1 course « Applied linear algebra », whose purpose is to present the algorithms and tools of matrix analysis necessary for machine learning and data processing. We will introduce the concepts and tools of multilinear algebra to analyze higher dimensional data. The latter are represented by tensors (multidimensional arrays) whose analysis can be done by methods generalizing matrix analysis techniques such as singular value decomposition. After the introduction of the mathematical formalism, the emphasis is put on the algorithmic aspects and applications.

Learning outcomes:

in progress

Indicative contents:

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

Methods of assessment:

Written test, practical work

Suggested bibliography:

in progress

Credits: 4
Language:

English

Course mode:

On-site

Methods of delivery:

Lectures (12h)

Tutorials (9h)

Practices (9h)

Pre-requisites:

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

Objectives:

Deep learning has become a must in artificial intelligence and more particularly in machine learning. The recent developments in machine translation, pattern recognition, speech recognition, autonomous driving and so on, are essentially due to the great advances made in this field. The goal of this course is to learn the basics of deep learning techniques and also to learn how to implement some elementary deep learning tasks. Each lesson will be followed by practical works with a Python3/JupyterLab environment, in order to use the deep learning tools as Tensorflow and Keras.

Learning outcomes:

in progress

Indicative contents:

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

Methods of assessment:

Written test, practical work

Suggested bibliography:

in progress

Credits: 4
Language:

English

Course mode:

On-site

Methods of delivery:

Lectures (12h)

Tutorials (9h)

Practices (9h)

Pre-requisites:

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

Objectives:

The many challenges posed by the machine learning and the processing of big and noisy data require the development of new mathematical tools and fast algorithms in optimization. The course starts with the class of Iterative Shrinkage-Thresholding Algorithms (ISTA) and their application for solving linear inverse problems in signal processing. This class of methods can be viewed as extension of the classical gradient algorithm and is known to be attractive due to their simplicity and adequacy for solving large-scale problems in optimization. We study their convergence analysis and also show their slowness in some situations. The Fast-Iterative Shrinkage-Thresholding Algorithm (FISTA) was introduced by Beck and Teboulle in 2009. The convergence analysis of FISTA will be studied in this lecture as well as its comparison with ISTA on several examples.

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.

Learning outcomes:

in progress

Indicative contents:

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

Methods of assessment:

Written test, practical work

Suggested bibliography:

in progress

Credits: 4
Language:

English

Course mode:

On-site

Methods of delivery:

Lectures (12h)

Tutorials (9h)

Practices (9h)

Pre-requisites:

Optimization basics, practical optimization and stochastic processes

Objectives:

We begin this course with the study of Markov decision processes. In this case, we assume that the decision-maker has full knowledge of the data of the problem and we talk about a model-based problem. Next, we drop this assumption, and we enter the realm of reinforcement learning problems, which loosely speaking means that the environment must be learnt from successive experiences. From the mathematical point of view, this can be done by using Monte-Carlo techniques, which will be studied in the course. In the second part of the course, we will present the theoretical foundations of stochastic optimization methods by introducing rigorously the so-called stochastic gradient descent and then proceeding to extend some standard first order algorithms in convex analysis to the case where randomness is present.

Learning outcomes:

in progress

Indicative contents:

Markov decision processes, stochastic algorithms, temporal differences, Q-learning.

Methods of assessment:

Written test, practical work

Suggested bibliography:

in progress

Credits: 4
Language:

English

Course mode:

On-site

Methods of delivery:

Lectures (12h)

Tutorials (9h)

Practices (9h)

Pre-requisites:

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

Objectives:

Chapter 0 recalls basics of convex analysis (such as projection and separation theorems, closed proper convex functions and Legendre-Fenchel conjugates). Chapter 1 explores fixed-point algorithms, as well as the relaxed Krasnoselskii-Mann algorihtm, for firmly nonexpansive and averaged operators (such as resolvents of maximal monotone operators). Applications are provided to projection operators with algorithms to solve convex feasibility problems. Chapter 2 introduces the classical notion of proximal operator associated to a closed proper convex function, which coincides with the resolvent of its subdifferential operator, and whose fixed points characterize its minimizers. The so-called proximal point algorithm is then invoked to solve convex minimization problems. In order to investigate sums and composites in the objective function, we investigate some well-known splitting methods, such as the proximal gradient algorithm (also called forward-backward algorithm) and the Douglas-Rachford algorithm. Finally Chapter 3 gives recalls on strong Lagrangian duality in convex inequality/equality constrained minimization problems and develops standard primal-dual methods, such as the method of multipliers or ADMM.

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.

Learning outcomes:

in progress

Indicative contents:

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

Methods of assessment:

Written test, practical work

Suggested bibliography:

in progress

Credits: 3
Language:

English

Course mode:

On-site

Methods of delivery:

Lectures (12h)

Tutorials (18h)

Pre-requisites:

in progress

Objectives:

in progress

Learning outcomes:

in progress

Indicative contents:

in progress

Methods of assessment:

Written test

Suggested bibliography:

in progress

Credits: 4
Language:

English

Course mode:

On-site

Methods of delivery:

Lectures (12h)

Tutorials (18h)

Pre-requisites:

in progress

Objectives:

in progress

Learning outcomes:

in progress

Indicative contents:

in progress

Methods of assessment:

Written test

Suggested bibliography:

in progress

Credits: 3
Language:

English

Course mode:

On-site

Methods of delivery:

Tutorials (30h)

Pre-requisites:

B1 level required.

Objectives:

To bring students towards the European B2/C1 level. The operational and evaluable objectives of this training are:

• Understand most situations that might be encountered at work or while traveling in a region where English is spoken for example
• Develop oral and written language skills
• International English communication

Learning outcomes:

Acquisition of English language skills (objective B2/C1). International, specialty and professional English (CV, cover letters, etc.)

Indicative contents:

• Written and oral comprehension/production work on authentic specialist or general English documents
• Interactive debates on general themes
• Language lab work (pronunciation, listening, repetition, etc.)
• Professional English (writing cover letters, CV, professional interview) academic (summary of documents, emails, sum-ups, etc.)
• Work on specialization and general English vocabulary.
• Presentation of a specialty presentation

Methods of assessment:

Written test, oral

Credits: 6
Language:

French/English

Course mode:

On-site/Hybrid

Methods of delivery:

Scientific project (one day/week)

Pre-requisites:

None

Objectives:

Carry a scientific or entrepreunarial project. 3 options:

• continue their « research » project carried out in M1 within the framework of the Cordées de la recherche
• carry out their project within the framework of the « Ateliers de l’innovation » offered by the IAE Limoges
• carry out their project in conjunction with a company, a CRT, a LabCom, etc.

Methods of assessment:

Project

Credits: 24
Language:

French/English

Course mode:

On-site

Methods of delivery:

6 months internship

Pre-requisites:

None

Objectives:

6 months training period in a company or in a research laboratory

Methods of assessment:

Report, oral, evaluation sheet