Mois : décembre 2024

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:

• pdf SLIDES
• arxiv version LINK
• published version LINK
• VIDEO.

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. 

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:

• pdf SLIDES
• arxiv version LINK
• published version LINK
• VIDEO.

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.