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 …
Neural networks-based algorithms for stochastic control and PDEs in finance
This chapter presents machine learning techniques and deep reinforcement learning-based
algorithms for the efficient resolution of nonlinear partial differential equations and dynamic …
algorithms for the efficient resolution of nonlinear partial differential equations and dynamic …
Generalization in mean field games by learning master policies
Abstract Mean Field Games (MFGs) can potentially scale multi-agent systems to extremely
large populations of agents. Yet, most of the literature assumes a single initial distribution for …
large populations of agents. Yet, most of the literature assumes a single initial distribution for …
Mean-field neural networks: learning mappings on Wasserstein space
We study the machine learning task for models with operators mapping between the
Wasserstein space of probability measures and a space of functions, like eg in mean-field …
Wasserstein space of probability measures and a space of functions, like eg in mean-field …
Actor-critic learning for mean-field control in continuous time
We study policy gradient for mean-field control in continuous time in a reinforcement
learning setting. By considering randomised policies with entropy regularisation, we derive a …
learning setting. By considering randomised policies with entropy regularisation, we derive a …
Universal approximation of symmetric and anti-symmetric functions
We consider universal approximations of symmetric and anti-symmetric functions, which are
important for applications in quantum physics, as well as other scientific and engineering …
important for applications in quantum physics, as well as other scientific and engineering …
Neural optimal stopping boundary
A method based on deep artificial neural networks and empirical risk minimization is
developed to calculate the boundary separating the stopping and continuation regions in …
developed to calculate the boundary separating the stopping and continuation regions in …
Rate of convergence for particle approximation of PDEs in Wasserstein space
We prove a rate of convergence for the N-particle approximation of a second-order partial
differential equation in the space of probability measures, such as the master equation or …
differential equation in the space of probability measures, such as the master equation or …
A fast iterative PDE-based algorithm for feedback controls of nonsmooth mean-field control problems
C Reisinger, W Stockinger, Y Zhang - SIAM Journal on Scientific Computing, 2024 - SIAM
We propose a PDE-based accelerated gradient algorithm for optimal feedback controls of
McKean–Vlasov dynamics that involve mean-field interactions both in the state and action …
McKean–Vlasov dynamics that involve mean-field interactions both in the state and action …
Deep backward and galerkin methods for the finite state master equation
A Cohen, M Laurière, E Zell - arXiv preprint arXiv:2403.04975, 2024 - arxiv.org
This paper proposes and analyzes two neural network methods to solve the master equation
for finite-state mean field games (MFGs). Solving MFGs provides approximate Nash …
for finite-state mean field games (MFGs). Solving MFGs provides approximate Nash …