相关论文: Deep Backward and Galerkin Methods for the Finite …

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean…

Mean-field games (MFG) were introduced to efficiently analyze approximate Nash equilibria in large population settings. In this work, we consider entropy-regularized mean-field games with a finite state-action space in a discrete time…

Recently proposed numerical algorithms for solving high-dimensional nonlinear partial differential equations (PDEs) based on neural networks have shown their remarkable performance. We review some of them and study their convergence…

This paper studies a large population dynamic game involving nonlinear stochastic dynamical systems with agents of the following mixed types: (i) a major agent, and (ii) a population of $N$ minor agents where $N$ is very large. The major…

Mean Field Games (MFGs) offer a powerful framework for studying large-scale multi-agent systems. Yet, learning Nash equilibria in MFGs remains a challenging problem, particularly when the initial distribution is unknown or when the…

For the classical backward induction algorithm, the input is an arbitrary $n$-person positional game with perfect information modeled by a finite acyclic directed graph (digraph) and the output is a profile $(x_1, \ldots, x_n)$ of pure…

We propose a new class of games, called Multi-Games (MG), in which a given number of players play a fixed number of basic games simultaneously. In each round of the MG, each player will have a specific set of weights, one for each basic…

The celebrated Krusel-Smith growth model is an important example of a Mean Field Game with a common noise. The Mean Field Game is encoded in the master equation, a partial differential equation satisfied by the value of the game which…

Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading…

We introduce Mean-Field Trust Region Policy Optimization (MF-TRPO), a novel algorithm designed to compute approximate Nash equilibria for ergodic Mean-Field Games (MFG) in finite state-action spaces. Building on the well-established…

We introduce a general framework for approximating parabolic Stochastic Partial Differential Equations (SPDEs) based on fluctuation-dissipation balance. Using this approach we formulate Stochastic Discontinuous Galerkin Methods (SDGM). We…

We examine global non-asymptotic convergence properties of policy gradient methods for multi-agent reinforcement learning (RL) problems in Markov potential games (MPG). To learn a Nash equilibrium of an MPG in which the size of state space…

Friedrichs' systems (FS) are symmetric positive linear systems of first-order partial differential equations (PDEs), which provide a unified framework for describing various elliptic, parabolic and hyperbolic semi-linear PDEs such as the…

A discontinuous Galerkin (dG) method for the numerical solution of initial/boundary value multi-compartment partial differential equation (PDE) models, interconnected with interface conditions, is presented and analysed. The study of…

In this paper, the generalized Nash equilibrium (GNE) seeking problem for continuous games with coupled affine inequality constraints is investigated in a partial-decision information scenario, where each player can only access its…

We propose a multiscale spectral generalized finite element method (MS-GFEM) for discontinuous Galerkin (DG) discretizations. The method builds local approximations on overlapping subdomains as the sum of a local source solution and a…

The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…

Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…

We use the Markov chain approximation method to construct approximations for the solution of the mean field game (MFG) with reflecting barriers studied in Bayraktar, Budhiraja, and Cohen (2017). The MFG is formulated in terms of a…