Add to ORKGIn this paper, we study a regularised relaxed optimal control problem and, in particular, we are concerned with the case where the control variable is of large dimension. We introduce a system of mean-field Langevin equations, the invariant measure of which is shown to be the optimal control of the initial problem under mild conditions. Therefore, this system of processes can be viewed as a continuous-time numerical algorithm for computing the optimal control. As an application, this result endorses the solvability of the stochastic gradient descent algorithm for a wide class of deep neural networks
We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural...
Best Paper AwardInternational audienceOne way to avoid overfitting in machine learning is to use mod...
For deterministic nonlinear dynamical systems, approximate dynamic programming based on Pontryagin\u...
In this paper, we study a regularised relaxed optimal control problem and, in particular, we are con...
We present a probabilistic analysis of the long-time behaviour of the nonlocal, diffusive equations ...
Two independent subjects are studied in this thesis, the first of which consists of two distinct pro...
International audienceIn this paper we consider a measure-theoretical formulation of the training of...
We study the optimal control in a long time horizon of neural ordinary differential equations which ...
International audienceIn this paper, we study a class of games regularized by relative entropy where...
Residual deep neural networks (ResNets) are mathematically described as interacting particle systems...
International audienceIn this paper we study a type of games regularized by the relative entropy, wh...
Minimizing non-convex and high-dimensional objective functions is challenging, especially when train...
We study a class of optimal stochastic control problems arising from the control of movements. Exact...
In this paper we model the role of a government of a large population as a mean field optimal contro...
In this paper, we explore the relation between distributionally robust learning and different forms ...
We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural...
Best Paper AwardInternational audienceOne way to avoid overfitting in machine learning is to use mod...
For deterministic nonlinear dynamical systems, approximate dynamic programming based on Pontryagin\u...
In this paper, we study a regularised relaxed optimal control problem and, in particular, we are con...
We present a probabilistic analysis of the long-time behaviour of the nonlocal, diffusive equations ...
Two independent subjects are studied in this thesis, the first of which consists of two distinct pro...
International audienceIn this paper we consider a measure-theoretical formulation of the training of...
We study the optimal control in a long time horizon of neural ordinary differential equations which ...
International audienceIn this paper, we study a class of games regularized by relative entropy where...
Residual deep neural networks (ResNets) are mathematically described as interacting particle systems...
International audienceIn this paper we study a type of games regularized by the relative entropy, wh...
Minimizing non-convex and high-dimensional objective functions is challenging, especially when train...
We study a class of optimal stochastic control problems arising from the control of movements. Exact...
In this paper we model the role of a government of a large population as a mean field optimal contro...
In this paper, we explore the relation between distributionally robust learning and different forms ...
We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural...
Best Paper AwardInternational audienceOne way to avoid overfitting in machine learning is to use mod...
For deterministic nonlinear dynamical systems, approximate dynamic programming based on Pontryagin\u...