Multi angle
Mean field type control with congestion
Auteurs : Laurière, Mathieu (Auteur de la Conférence)
CIRM (Editeur )
CIRM (Editeur )
- [Multi angle] Forward and backward simulation of Euler scheme / Auteur de la Conférence Gobet, Emmanuel.
- [Multi angle] Stochastic variational inequalities for random mechanics / Auteur de la Conférence Mertz, Laurent.
- [Multi angle] On the discretization of some nonlinear Fokker-Planck-Kolmogorov equations and applications / Auteur de la Conférence Silva Álvarez, Francisco José.
- [Multi angle] Project evaluation under uncertainty / Auteur de la Conférence Zubelli, Jorge P..
- [Multi angle] Some asymptotic results about American options and volativity / Auteur de la Conférence De Marco, Stefano.
- [Multi angle] Projected particle methods for solving McKean Vlasov SDEs / Auteur de la Conférence Belomestny, Denis.
- [Multi angle] Splitting algorithm for nested events / Auteur de la Conférence Goudenège, Ludovic.
- [Multi angle] Lecture 2: Introduction to HPC - MPI: design of parallel program and MPI / Auteur de la Conférence Lelong, Jérôme.
- [Multi angle] Lecture 1: Introduction to HPC, random generation, and OpenMP / Auteur de la Conférence Lelong, Jérôme.
- [ Post-edited] Numerical methods for mean field games - Lecture 2: Monotone finite difference schemes / Auteur de la Conférence Achdou, Yves.
- [Multi angle] Numerical methods for mean field games - Lecture 3: Variational MFG and related algorithms for solving the discrete system of nonlinear equations / Auteur de la Conférence Achdou, Yves.
- [Multi angle] Numerical methods for mean field games - Lecture 1: Introduction to the system of PDEs and its interpretation. Uniqueness of classical solutions / Auteur de la Conférence Achdou, Yves.
- [Multi angle] Metamodels for uncertainty quantification and reliability analysis / Auteur de la Conférence Marelli, Stefano.
- [Multi angle] Global sensitivity analysis in stochastic systems / Auteur de la Conférence Le Maître, Olivier.
- [Multi angle] Subsurface flow with uncertainty : applications and numerical analysis issues / Auteur de la Conférence Charrier, Julia.
- [Multi angle] Dynamic formulations of optimal transportation and variational MFGs / Auteur de la Conférence Benamou, Jean-David.
- [Multi angle] Least squares regression Monte Carlo for approximating BSDES and semilinear PDES / Auteur de la Conférence Turkedjiev, Plamen.
- [Multi angle] Bandits in auctions (& more) / Auteur de la Conférence Perchet, Vianney.
- [Multi angle] Multilevel and multi-index sampling methods with applications - Lecture 2: Multilevel and Multi-index Monte Carlo methods for the McKean-Vlasov equation / Auteur de la Conférence Tempone, Raul.
- [Multi angle] Multilevel and multi-index sampling methods with applications - Lecture 1: Adaptive strategies for Multilevel Monte Carlo / Auteur de la Conférence Tempone, Raul.
- [Multi angle] Model-free control and deep learning / Auteur de la Conférence Bellemare, Marc.
- [Multi angle] Optimal vector quantization: from signal processing to clustering and numerical probability / Auteur de la Conférence Pagès, Gilles.
- [Multi angle] The Metropolis Hastings algorithm: introduction and optimal scaling of the transient phase / Auteur de la Conférence Jourdain, Benjamin.
- [Multi angle] Branching for PDEs / Auteur de la Conférence Warin, Xavier.
- [Multi angle] On the interplay between kinetic theory and game theory / Auteur de la Conférence Degond, Pierre.
- [Multi angle] Particle algorithm for McKean SDE: a short review on numerical analysis / Auteur de la Conférence Bossy, Mireille.
- [Multi angle] Cubature methods and applications / Auteur de la Conférence Crisan, Dan.
- [Multi angle] Capacity expansion games with application to competition in power generation investments / Auteur de la Conférence Aïd, René.
- [Multi angle] An introduction to BSDE / Auteur de la Conférence Imkeller, Peter.
- [Multi angle] Mean field games with major and minor players / Auteur de la Conférence Carmona, René.
- Achdou, Y., & Laurière, M. (2016). Mean field type control with congestion. Applied Mathematics and Optimization, 73(3), 393-418 - http://dx.doi.org/10.1007/s00245-016-9342-8
- Achdou, Y., & Laurière, M. (2016). Mean field type control with congestion. II: An augmented Lagrangian method. Applied Mathematics and Optimization, 74(3), 535-578 - http://dx.doi.org/10.1007/s00245-016-9391-z
Loading the player...
Résumé :
The theory of mean field type control (or control of MacKean-Vlasov) aims at describing the behaviour of a large number of agents using a common feedback control and interacting through some mean field term. The solution to this type of control problem can be seen as a collaborative optimum. We will present the system of partial differential equations (PDE) arising in this setting: a forward Fokker-Planck equation and a backward Hamilton-Jacobi-Bellman equation. They describe respectively the evolution of the distribution of the agents' states and the evolution of the value function. Since it comes from a control problem, this PDE system differs in general from the one arising in mean field games.
Recently, this kind of model has been applied to crowd dynamics. More precisely, in this talk we will be interested in modeling congestion effects: the agents move but try to avoid very crowded regions. One way to take into account such effects is to let the cost of displacement increase in the regions where the density of agents is large. The cost may depend on the density in a non-local or in a local way. We will present one class of models for each case and study the associated PDE systems. The first one has classical solutions whereas the second one has weak solutions. Numerical results based on the Newton algorithm and the Augmented Lagrangian method will be presented.
This is joint work with Yves Achdou.
Codes MSC : Recently, this kind of model has been applied to crowd dynamics. More precisely, in this talk we will be interested in modeling congestion effects: the agents move but try to avoid very crowded regions. One way to take into account such effects is to let the cost of displacement increase in the regions where the density of agents is large. The cost may depend on the density in a non-local or in a local way. We will present one class of models for each case and study the associated PDE systems. The first one has classical solutions whereas the second one has weak solutions. Numerical results based on the Newton algorithm and the Augmented Lagrangian method will be presented.
This is joint work with Yves Achdou.
35K40 - Second-order parabolic systems
35K55 - Nonlinear parabolic equations
35K65 - Parabolic equations of degenerate type
49K20 - Optimal control problems with PDE (optimality conditions)
65K10 - Optimization and variational techniques
65M06 - Finite difference methods (IVP of PDE)
35D30 - Weak solutions of PDE
49N70 - Differential games in calculus of variations
|
Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 10/08/17 Date de captation : 09/08/17 Collection : Research talks ; Control Theory and Optimization ; Partial Differential Equations ; Numerical Analysis and Scientific Computing Format : MP4 Durée : 00:47:28 Domaine : PDE ; Control Theory & Optimization ; Numerical Analysis & Scientific Computing Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2017-08-09_Lauriere.mp4 
|
Informations sur la rencontre
Nom de la rencontre : CEMRACS: Numerical methods for stochastic models: control, uncertainty quantification, mean-field / CEMRACS : Méthodes numériques pour équations stochastiques : contrôle, incertitude, champ moyenOrganisateurs de la rencontre : Bouchard, Bruno ; Chassagneux, Jean-François ; Delarue, François ; Gobet, Emmanuel ; Lelong, Jérôme Dates : 17/07/17 - 25/08/17 Année de la rencontre : 2017 URL Congrès : http://conferences.cirm-math.fr/1556.html Citation Data
DOI : 10.24350/CIRM.V.19205403Cite this video as: Laurière, Mathieu (2017). Mean field type control with congestion. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19205403 URI : http://dx.doi.org/10.24350/CIRM.V.19205403 |
Voir aussi
Bibliographie
Z
