An algebraic convergence rate for the optimal control of McKean–Vlasov dynamics
We establish an algebraic rate of convergence of the value functions of-particle stochastic
control problems towards the value function of the corresponding McKean–Vlasov problem …
control problems towards the value function of the corresponding McKean–Vlasov problem …
Viscosity solutions for mckean–vlasov control on a torus
HM Soner, Q Yan - SIAM Journal on Control and Optimization, 2024 - SIAM
An optimal control problem in the space of probability measures and the viscosity solutions
of the corresponding dynamic programming equations defined using the intrinsic linear …
of the corresponding dynamic programming equations defined using the intrinsic linear …
Comparison of viscosity solutions for a class of second order PDEs on the Wasserstein space
We prove a comparison result for viscosity solutions of second order parabolic partial
differential equations in the Wasserstein space. The comparison is valid for semisolutions …
differential equations in the Wasserstein space. The comparison is valid for semisolutions …
From finite population optimal stopping to mean field optimal stopping
This paper analyzes the convergence of the finite population optimal stopping problem
towards the corresponding mean field limit. Building on the viscosity solution …
towards the corresponding mean field limit. Building on the viscosity solution …
Sharp convergence rates for mean field control in the region of strong regularity
P Cardaliaguet, J Jackson… - arXiv preprint arXiv …, 2023 - arxiv.org
We study the convergence problem for mean field control, also known as optimal control of
McKean-Vlasov dynamics. We assume that the data is smooth but not convex, and thus the …
McKean-Vlasov dynamics. We assume that the data is smooth but not convex, and thus the …
Quantitative propagation of chaos for mean field Markov decision process with common noise
We investigate propagation of chaos for mean field Markov Decision Process with common
noise (CMKV-MDP), and when the optimization is performed over randomized open-loop …
noise (CMKV-MDP), and when the optimization is performed over randomized open-loop …
Generalized pair-wise logit dynamic and its connection to a mean field game: theoretical and computational investigations focusing on resource management
H Yoshioka, M Tsujimura - Dynamic Games and Applications, 2024 - Springer
Logit dynamics are evolution equations that describe transitions to equilibria of actions
among many players. We formulate a pair-wise logit dynamic in a continuous action space …
among many players. We formulate a pair-wise logit dynamic in a continuous action space …
Mean field approximation of an optimal control problem for the continuity equation arising in smart charging
A Seguret - Applied Mathematics & Optimization, 2023 - Springer
We consider the optimal control of a finite population of hybrid processes (namely agents
state is composed of a discrete and a continuous variable), modeling the optimal charging of …
state is composed of a discrete and a continuous variable), modeling the optimal charging of …
Finite approximations for mean field type multi-agent control and their near optimality
E Bayraktar, N Bauerle, AD Kara - arXiv preprint arXiv:2211.09633, 2022 - arxiv.org
We study a multi-agent mean field type control problem in discrete time where the agents
aim to find a socially optimal strategy and where the state and action spaces for the agents …
aim to find a socially optimal strategy and where the state and action spaces for the agents …
A finite-dimensional approximation for partial differential equations on Wasserstein space
M Talbi - Stochastic Processes and their Applications, 2024 - Elsevier
This paper presents a finite-dimensional approximation for a class of partial differential
equations on the space of probability measures. These equations are satisfied in the sense …
equations on the space of probability measures. These equations are satisfied in the sense …