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 …

Inverse problems for mean field games

H Liu, C Mou, S Zhang - Inverse Problems, 2023 - iopscience.iop.org
The theory of mean field games (MFGs) studies the limiting behaviors of large systems
where the agents interact with each other in a certain symmetric way. The running and …

A numerical algorithm for inverse problem from partial boundary measurement arising from mean field game problem

YT Chow, SW Fung, S Liu, L Nurbekyan… - Inverse …, 2022 - iopscience.iop.org
In this work, we consider a novel inverse problem in mean-field games (MFGs). We aim to
recover the MFG model parameters that govern the underlying interactions among the …

Mean-field Markov decision processes with common noise and open-loop controls

M Motte, H Pham - The Annals of Applied Probability, 2022 - projecteuclid.org
We develop an exhaustive study of Markov decision process (MDP) under mean field
interaction both on states and actions in the presence of common noise, and when …

Reinforcement learning for mean field games, with applications to economics

A Angiuli, JP Fouque, M Lauriere - arxiv preprint arxiv:2106.13755, 2021 - cambridge.org
Mean field games (MFG) and mean field control problems (MFC) are frameworks to study
Nash equilibria or social optima in games with a continuum of agents. These problems can …

Closed-loop convergence for mean field games with common noise

D Lacker, L Le Flem - The Annals of Applied Probability, 2023 - projecteuclid.org
This paper studies the convergence problem for mean field games with common noise. We
define a suitable notion of weak mean field equilibria, which we prove captures all …

Propagation of chaos of forward–backward stochastic differential equations with graphon interactions

E Bayraktar, R Wu, X Zhang - Applied Mathematics & Optimization, 2023 - Springer
In this paper, we study graphon mean field games using a system of forward–backward
stochastic differential equations. We establish the existence and uniqueness of solutions …

Mean field control and finite agent approximation for regime-switching jump diffusions

E Bayraktar, A Cecchin, P Chakraborty - Applied Mathematics & …, 2023 - Springer
We consider a jump-diffusion mean field control problem with regime switching in the state
dynamics. The corresponding value function is characterized as the unique viscosity …

Quantitative convergence for displacement monotone mean field games with controlled volatility

J Jackson, L Tangpi - Mathematics of Operations Research, 2024 - pubsonline.informs.org
We study the convergence problem for mean field games with common noise and controlled
volatility. We adopt the strategy recently put forth by Laurière and the second author, using …

Extended mean field control problem: a propagation of chaos result

MF Djete - Electronic Journal of Probability, 2022 - projecteuclid.org
In this paper, we study the extended mean field control problem, which is a class of McKean–
Vlasov stochastic control problem where the state dynamics and the reward functions …