相关论文: Mean-field neural networks-based algorithms for Mc…
In this article, we prove the existence of weak solutions as well as the existence and uniqueness of strong solutions for McKean-Vlasov multivalued stochastic differential equations with oblique subgradients (MVMSDEswOS, for short) by means…
We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…
This paper is devoted to a viscosity solution theory of the stochastic Hamilton-Jacobi-Bellman equation in the Wasserstein spaces for the mean-field type control problem which allows for random coefficients and may thus be non-Markovian.…
Mean-field backward doubly stochastic differential equations (MF-BDSDEs, for short) are introduced and studied. The existence and uniqueness of solutions for MF-BDSDEs is established. One probabilistic interpretation for the solutions to a…
We present the particle method for simulating the solution to the path-dependent McKean-Vlasov equation, in which both the drift and the diffusion coefficients depend on the whole trajectory of the process up to the current time t, as well…
We study a mean field optimal control problem with general non-Markovian dynamics, including both common noise and jumps. We show that its minimizers are Nash equilibria of an associated mean field game of controls. These types of games are…
We consider extended mean-field control problems with multi-dimensional singular controls. A key challenge when analysing singular controls are jump costs. When controls are one-dimensional, jump costs are most naturally computed by linear…
In this paper, how to successfully and efficiently condition a target population of agents towards consensus is discussed. To overcome the curse of dimensionality, the mean field formulation of the consensus control problem is considered.…
In recent years, reinforcement learning and its multi-agent analogue have achieved great success in solving various complex control problems. However, multi-agent reinforcement learning remains challenging both in its theoretical analysis…
We propose a novel data-driven neural network (NN) optimization framework for solving an optimal stochastic control problem under stochastic constraints. Customized activation functions for the output layers of the NN are applied, which…
We propose a novel approach to numerically approximate McKean-Vlasov stochastic differential equations (MV-SDE) using stochastic gradient descent (SGD) while avoiding the use of interacting particle systems (IPS) {and the associated…
We design a fully implementable scheme to compute the invariant distribution of ergodic McKean-Vlasov SDE satisfying a uniform confluence property. Under natural conditions, we prove various convergence results notably we obtain rates for…
The mean field variational inference (MFVI) formulation restricts the general Bayesian inference problem to the subspace of product measures. We present a framework to analyze MFVI algorithms, which is inspired by a similar development for…
In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. We discuss the well-posedness of the multi-species SDE system,…
Integrating measurements and historical data can enhance control systems through learning-based techniques, but ensuring performance and safety is challenging. Robust model predictive control strategies, like stochastic model predictive…
This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…
This work focuses on the mean field stochastic partial differential equations with nonlinear kernels. We first prove the existence and uniqueness of strong and weak solutions for mean field stochastic partial differential equations in the…
Supervised convolutional neural networks (CNNs) are widely used to solve imaging inverse problems, achieving state-of-the-art performance in numerous applications. However, despite their empirical success, these methods are poorly…
Decentralized stochastic control (DSC) considers the optimal control problem of a multi-agent system. However, DSC cannot be solved except in the special cases because the estimation among the agents is generally intractable. In this work,…
In this paper, we study the linear-quadratic control problem for mean-field backward stochastic differential equations (MF-BSDE) with random coefficients. We first derive a preliminary stochastic maximum principle to analyze the unique…