Recent developments in machine learning methods for stochastic control and games
R Hu, M Lauriere - arXiv preprint arXiv:2303.10257, 2023 - arxiv.org
Stochastic optimal control and games have a wide range of applications, from finance and
economics to social sciences, robotics, and energy management. Many real-world …
economics to social sciences, robotics, and energy management. Many real-world …
[图书][B] Probabilistic theory of mean field games with applications I-II
The lion's share of this chapter is devoted to the construction of equilibria for mean field
games with a common noise. We develop a general two-step strategy for the search of weak …
games with a common noise. We develop a general two-step strategy for the search of weak …
Fictitious play for mean field games: Continuous time analysis and applications
S Perrin, J Pérolat, M Laurière… - Advances in neural …, 2020 - proceedings.neurips.cc
In this paper, we deepen the analysis of continuous time Fictitious Play learning algorithm to
the consideration of various finite state Mean Field Game settings (finite horizon, $\gamma …
the consideration of various finite state Mean Field Game settings (finite horizon, $\gamma …
Mean field games
PE Caines - Encyclopedia of systems and control, 2021 - Springer
The notion of the infinite population limit of large population games where agents are
realized by controlled stochastic dynamical systems is introduced. The theory of infinite …
realized by controlled stochastic dynamical systems is introduced. The theory of infinite …
Mean field game of controls and an application to trade crowding
P Cardaliaguet, CA Lehalle - Mathematics and Financial Economics, 2018 - Springer
In this paper we formulate the now classical problem of optimal liquidation (or optimal
trading) inside a mean field game (MFG). This is a noticeable change since usually …
trading) inside a mean field game (MFG). This is a noticeable change since usually …
Convergence analysis of machine learning algorithms for the numerical solution of mean field control and games: II—the finite horizon case
R Carmona, M Laurière - The Annals of Applied Probability, 2022 - projecteuclid.org
We propose two numerical methods for the optimal control of McKean–Vlasov dynamics in
finite time horizon. Both methods are based on the introduction of a suitable loss function …
finite time horizon. Both methods are based on the introduction of a suitable loss function …
Scalable deep reinforcement learning algorithms for mean field games
Abstract Mean Field Games (MFGs) have been introduced to efficiently approximate games
with very large populations of strategic agents. Recently, the question of learning equilibria …
with very large populations of strategic agents. Recently, the question of learning equilibria …
[图书][B] Lectures on BSDEs, stochastic control, and stochastic differential games with financial applications
R Carmona - 2016 - SIAM
This book grew out of the lecture notes I prepared for a graduate class I taught at Princeton
University in 2011–12, and again in 2012–13. My goal was to introduce the students to …
University in 2011–12, and again in 2012–13. My goal was to introduce the students to …
Dynamic programming for optimal control of stochastic McKean--Vlasov dynamics
H Pham, X Wei - SIAM Journal on Control and Optimization, 2017 - SIAM
We study optimal control of the general stochastic McKean--Vlasov equation. Such a
problem is motivated originally from the asymptotic formulation of cooperative equilibrium for …
problem is motivated originally from the asymptotic formulation of cooperative equilibrium for …