相关论文: A hybrid deep learning method for finite-horizon m…

We introduce a novel framework to model and solve mean-field game systems with nonlocal interactions. Our approach relies on kernel-based representations of mean-field interactions and feature-space expansions in the spirit of kernel…

In this paper, we study the vehicle routing problem with a finite time horizon. In this routing problem, the objective is to maximize the number of customer requests served within a finite time horizon. We present a novel routing network…

The paper is concerned with the approximation of the deterministic the mean field type control system by a mean field Markov chain. It turns out that the dynamics of the distribution in the approximating system is described by a system of…

This paper studies the problem of parameter learning in probabilistic graphical models having latent variables, where the standard approach is the expectation maximization algorithm alternating expectation (E) and maximization (M) steps.…

We extend the methods from Nurbekyan, Saude "Fourier approximation methods for first-order nonlocal mean-field games" [Port. Math. 75 (2018), no. 3-4] and Liu, Jacobs, Li, Nurbekyan, Osher "Computational methods for nonlocal mean field…

Mean Field Games (MFGs) have been introduced to efficiently approximate games with very large populations of strategic agents. Recently, the question of learning equilibria in MFGs has gained momentum, particularly using model-free…

In the literature, existence of mean-field equilibria has been established for discrete-time mean field games under both the discounted cost and the average cost optimality criteria. In this paper, we provide a value iteration algorithm to…

We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast…

Q-learning is a popular reinforcement learning algorithm. This algorithm has however been studied and analysed mainly in the infinite horizon setting. There are several important applications which can be modeled in the framework of finite…

This paper studies the convergence of mean field games with finite state space to mean field games with a continuous state space. We examine a space discretization of a diffusive dynamics, which is reminiscent of the Markov chain…

This paper introduces Deep Policy Iteration (DPI), a novel approach that integrates the strengths of Neural Networks with the stability and convergence advantages of Policy Iteration (PI) to address high-dimensional stochastic Mean Field…

Many real-world phenomena can be modelled as dynamical processes on networks, a prominent example being the spread of infectious diseases such as COVID-19. Mean-field approximations are a widely used tool to analyse such dynamical processes…

Multi-agent reinforcement learning, despite its popularity and empirical success, faces significant scalability challenges in large-population dynamic games. Graphon mean field games (GMFGs) offer a principled framework for approximating…

Markov Chain Monte Carlo (MCMC) algorithms are widely used for stochastic optimization, sampling, and integration of mathematical objective functions, in particular, in the context of Bayesian inverse problems and parameter estimation. For…

The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…

This paper proposes a machine-learning-based solution approach for solving multi-horizon stochastic programs. The approach embeds a deep learning neural network into a multi-horizon stochastic program to approximate the recourse operational…

We consider the problem of simultaneous learning in stochastic games with many players in the finite-horizon setting. While the typical target solution for a stochastic game is a Nash equilibrium, this is intractable with many players. We…

Statistical inference methods are fundamentally important in machine learning. Most state-of-the-art inference algorithms are variants of Markov chain Monte Carlo (MCMC) or variational inference (VI). However, both methods struggle with…

One of the core problems in mean-field control and mean-field games is to solve the corresponding McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs). Most existing methods are tailored to special cases in which the…

We study deterministic optimal control problems for differential games with finite horizon. We propose new approximations of the strategies in feedback form, and show error estimates and a convergence result of the value in some weak sense…