Auteur : gabriel

Analyse numérique: évolution (M1 Math, Université Paris Dauphine – PSL, 2005-11, 2019-2025

gabriel

Responsable de cours: Gabriel TURINICI
Contenu:
1 Introduction
2 EDO
3 Calcul de dérivée et contrôle
4 EDS
Bibliographie: poly distribué

Documents de support de cours, autres documents

NOTA BENE: Tous des documents sont soumis au droit d’auteur, et ne peuvent pas être distribués sauf accord préalable ÉCRIT de l’auteur.

Supports de cours: livre en anglais « Numerical simulations of time-dependent problems : applied to epidemiology, artificial intelligence and finance »

Implementations TP:

EDO: exo sur la précision, exo stabilité , SIR(EE+H+RK4),  order for the EE/H schemes/SIR

SIR (version controle, adjoint / backward); (version 2023 here)

EDS version 2025 : implémenter : 

1/ simulation brownien

2/ calcul intégrale de W par/rapport à W

3/ calcul par Euler-Maruyama pour équation d’Ornstein-Uhlenbeck

4/ calcul par Euler-Maruyama faible pour modèle log-normal (Black-Scholes)

Version anciennes

2022/23:

2020/21:

« Convergence of a L2 regularized Policy Gradient Algorithm for the Multi Armed Bandit » at ICPR 2024

gabriel

This joint work with Stefana-Lucia ANITA has been presented at the at the 27th International Conference on Pattern Recognition (ICPR) 2024 held in Kolkata, India, Dec 1st through 5th 2024.

Talk materials:

Abstract : Although Multi Armed Bandit (MAB) on one hand and the policy gradient approach on the other hand are among the most used frameworks of Reinforcement Learning, the theoretical properties of the policy gradient algorithm used for MAB have not been given enough attention. We investigate in this work the convergence of such a procedure for the situation when a L2 regularization term is present jointly with the ‘softmax’ parametrization. We prove convergence under appropriate technical hypotheses and test numerically the procedure including situations beyond the theoretical setting. The tests show that a time dependent regularized procedure can improve over the canonical approach especially when the initial guess is far from the solution. 

« Optimal time sampling in physics-informed neural networks » at ICPR 2024

gabriel

This talk has been presented at the at the 27th International Conference on Pattern Recognition (ICPR) 2024 held in Kolkata, India, Dec 1st through 5th 2024.

Talk materials:

Abtract : Physics-informed neural networks (PINN) is a extremely powerful paradigm used to solve equations encountered in scientific computing applications. An important part of the procedure is the minimization of the equation residual which includes, when the equation is time-dependent, a time sampling. It was argued in the literature that the sampling need not be uniform but should overweight initial time instants, but no rigorous explanation was provided for this choice. In the present work we take some prototypical examples and, under standard hypothesis concerning the neural network convergence, we show that the optimal time sampling follows a (truncated) exponential distribution. In particular we explain when is best to use uniform time sampling and when one should not. The findings are illustrated with numerical examples on linear equation, Burgers’ equation and the Lorenz system.

General chair of the conference FAAI24 « Foundations and applications of artificial intelligence », Iasi, October 28-30, 2024

gabriel

General chair with C. Lefter and A. Zalinescu of the conference FAAI24 « Foundations and applications of artificial intelligence » Iasi Oct 28-30 2024. At the conference I also serve as tutorial presenter.

LLM and time series at the « 6th J.P. Morgan Global Machine Learning Conference », Paris, Oct 18th, 2024

gabriel

Invited joint talk « Using LLMs techniques for time series prediction » with Pierre Brugiere presented at the 6th JP Morgan Global Machine Learning conference held in Paris, Oct 18th 2024

Talk materials: slides(click here) and here a link to the associated paper.

Interview with radio « France Culture » on the ethics of generative AI

gabriel

A short interview with Celine Loozen from ‘France Culture’ radio station within a radio program concerning AI and GAFAM ethics.

Link for the full radio broadcast

Interview with Celine Loozen : here (local version if necessary here)

Reinforcement Learning, M2 ISF App, 2021-2025

gabriel

Instructor: Gabriel TURINICI


1/ Introduction to reinforcement learning
2/ Theoretical formalism: Markov decision processes (MDP), value function ( Belman and Hamilton- Jacobi – Bellman equations) etc.
3/ Common strategies, building from the example of « multi-armed bandit »
4/ Strategies in deep learning: Q-learning and DQN
5/ Strategies in deep learning: SARSA and variants
6/ Strategies in deep learning: Actor-Critic and variants
7/ During the course: various Python and gym/gymnasium implementations
8/ Perspectives.

Principal document for the theoretical presentations: (no distribution autoried without WRITTEN consent from the author)

Multi Armed Bandit codes (MAB) : play MAB, solve MAB , solve MAB v2., policy grad from chatGPT to correct., policy grad corrected.

Bellman iterations: code to correct here, solution code here

Gym: play Frozen Lake (v2023) (version 2022)

Q-Learning : with Frozen Lake, python version or notebook version

-play with gym/Atari-Breakout: python version or notebook version

Deep Q Learning (DQN) : Learn with gym/Atari-Breakout: notebook 2024 and its version with smaller NN and play with result

Policy gradients on Pong adapted from Karpathy, 2024 version (correct to get it working!) python or notebook

You can also load from HERE a converged version (rename as necessary) pg_pong_converged_turinici24

Notebook to use it: here (please send me yours if mean reward above 15!).

Projets : cf. Teams