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 …

This chapter presents machine learning techniques and deep reinforcement learning-based
algorithms for the efficient resolution of nonlinear partial differential equations and dynamic …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …