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We consider adaptive finite element methods (AFEMs) with inexact algebraic solvers for second-order symmetric linear elliptic diffusion problems. Optimal complexity of AFEM, i.e., optimal convergence rates with respect to the overall…

Numerical Analysis · Mathematics 2026-04-10 Paula Hilbert , Ani Miraçi , Dirk Praetorius

In this paper, we propose an initial value fomulation of the discrete mean field games on finite graphs (Graph MFG), and design a neural network based approach to solve it. Graph MFG describes infinite, non-cooperative and interactive…

Numerical Analysis · Mathematics 2026-04-08 Yaxin Feng , Yang Xiang , Haomin Zhou

First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results…

Analysis of PDEs · Mathematics 2022-07-12 Megan Griffin-Pickering , Alpár R. Mészáros

We propose a novel generalization of the conditional gradient (CG / Frank-Wolfe) algorithm for minimizing a smooth function $f$ under an intersection of compact convex sets, using a first-order oracle for $\nabla f$ and linear minimization…

Optimization and Control · Mathematics 2024-10-11 Zev Woodstock , Sebastian Pokutta

Softmax policy gradient is a popular algorithm for policy optimization in single-agent reinforcement learning, particularly since projection is not needed for each gradient update. However, in multi-agent systems, the lack of central…

Optimization and Control · Mathematics 2022-11-01 Runyu Zhang , Jincheng Mei , Bo Dai , Dale Schuurmans , Na Li

We establish the convergence of the deep actor-critic reinforcement learning algorithm presented in [Angiuli et al., 2023a] in the setting of continuous state and action spaces with an infinite discrete-time horizon. This algorithm provides…

Optimization and Control · Mathematics 2025-11-11 Jean-Pierre Fouque , Mathieu Laurière , Mengrui Zhang

The globally convergent convexification numerical method is constructed for a Coefficient Inverse Problem for the Mean Field Games System. A coefficient characterizing the global interaction term is recovered from the single measurement…

Numerical Analysis · Mathematics 2023-10-16 Michael V. Klibanov , Jingzhi Li , Zhipeng Yang

In the presence of a common noise, we study the convergence problems in mean field game (MFG) and mean field control (MFC) problem where the cost function and the state dynamics depend upon the joint conditional distribution of the…

Probability · Mathematics 2023-08-29 Mao Fabrice Djete

In this note we propose a transformation which decouples stationary Mean Field Games systems with superlinear Hamiltonians of the form |p|^r, and turns the Hamilton-Jacobi-Bellman equation into a quasi-linear equation involving the…

Analysis of PDEs · Mathematics 2015-05-25 Marco Cirant

In this work, we study the convergence rate of the $N$-player LQG game with a Markov chain common noise towards its asymptotic Mean Field Game. By postulating a Markovian structure via two auxiliary processes for the first and second…

Optimization and Control · Mathematics 2023-08-30 Jiamin Jian , Peiyao Lai , Qingshuo Song , Jiaxuan Ye

We extend the weak-strong uniqueness principle for mean-field game (MFG) systems to a broad class of second-order stationary and time-dependent problems. Under standard monotonicity, growth, and coercivity assumptions on the Hamiltonian,…

Analysis of PDEs · Mathematics 2026-04-02 Rita Ferreira , Diogo Gomes , Bashayer Majrashi

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…

Optimization and Control · Mathematics 2018-08-28 Erhan Bayraktar , Amarjit Budhiraja , Asaf Cohen

Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we…

Machine Learning · Statistics 2024-06-27 Cencheng Shen , Carey E. Priebe , Joshua T. Vogelstein

We investigate multi-agent imitation learning (IL) within the framework of mean field games (MFGs), considering the presence of time-varying correlated signals. Existing MFG IL algorithms assume demonstrations are sampled from Mean Field…

Multiagent Systems · Computer Science 2024-10-04 Zhiyu Zhao , Qirui Mi , Ning Yang , Xue Yan , Haifeng Zhang , Jun Wang , Yaodong Yang

In this paper we propose a splitting scheme which hybridizes generalized conditional gradient with a proximal step which we call CGALP algorithm, for minimizing the sum of three proper convex and lower-semicontinuous functions in real…

Optimization and Control · Mathematics 2022-10-20 Antonio Silveti-Falls , Cesare Molinari , Jalal Fadili

We prove a rate of convergence for finite element approximations of stationary, second-order mean field games with nondifferentiable Hamiltonians posed in general bounded polytopal Lipschitz domains with strongly monotone running costs. In…

Numerical Analysis · Mathematics 2026-03-20 Yohance A. P. Osborne , Iain Smears

In this paper we present a numerical scheme to solve coupled mean field forward-backward stochastic differential equations driven by monotone vector fields. This is based on an adaptation of so called extragradient methods by characterizing…

Optimization and Control · Mathematics 2026-03-17 Charles Meynard

A mean-field game (MFG) seeks the Nash Equilibrium of a game involving a continuum of players, where the Nash Equilibrium corresponds to a fixed point of the best-response mapping. However, simple fixed-point iterations do not always…

Optimization and Control · Mathematics 2025-07-15 Jiajia Yu , Xiuyuan Cheng , Jian-Guo Liu , Hongkai Zhao

Here, we establish the existence of weak solutions to a wide class of time-dependent monotone mean-field games (MFGs). These MFGs are given as a system of degenerate parabolic equations with initial and terminal conditions. To construct…

Analysis of PDEs · Mathematics 2020-01-14 Rita Ferreira , Diogo Gomes , Teruo Tada

We consider payoff-based learning of a generalized Nash equilibrium (GNE) in multi-agent systems. Our focus is on games with jointly convex constraints of a linear structure and strongly monotone pseudo-gradients. We present a convergent…

Optimization and Control · Mathematics 2025-07-18 Tatiana Tatarenko , Maryam Kamgarpour