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Reinforcement learning is a powerful tool to learn the optimal policy of possibly multiple agents by interacting with the environment. As the number of agents grow to be very large, the system can be approximated by a mean-field problem.…

Optimization and Control · Mathematics 2020-08-18 Weichen Wang , Jiequn Han , Zhuoran Yang , Zhaoran Wang

In this paper, we study a linear-quadratic optimal control problem for mean-field stochastic differential equations driven by a Poisson random martingale measure and a multidimensional Brownian motion. Firstly, the existence and uniqueness…

Optimization and Control · Mathematics 2016-10-12 Maoning Tang , Qingxin Meng

The large-population system consists of considerable small agents whose individual behavior and mass effect are interrelated via their state-average. The mean-field game provides an efficient way to get the decentralized strategies of…

Optimization and Control · Mathematics 2014-03-25 Jianhui Huang , Shujun Wang

In this paper we model the role of a government of a large population as a mean field optimal control problem. Such control problems are constrainted by a PDE of continuity-type, governing the dynamics of the probability distribution of the…

Optimization and Control · Mathematics 2016-08-08 Giacomo Albi , Young-Pil Choi , Massimo Fornasier , Dante Kalise

We investigate a stochastic differential game in which a major player has a private information (the knowledge of a random variable), which she discloses through her control to a population of small players playing in a Nash Mean Field Game…

Optimization and Control · Mathematics 2023-11-28 Philippe Bergault , Pierre Cardaliaguet , Catherine Rainer

We develop a variational approach to address risk-sensitive optimal control problems with an exponential-of-integral cost functional in a general linear-quadratic-Gaussian (LQG) single-agent setup, offering new insights into such problems.…

Optimization and Control · Mathematics 2025-03-28 Hanchao Liu , Dena Firoozi , Michèle Breton

Motivated by a product pricing problem, a linear-quadratic Stackelberg differential game for a regime switching system involving one leader and two followers is studied. The two followers engage in a zero-sum differential game, and both the…

Optimization and Control · Mathematics 2026-03-31 Pengyan Huang , Na Li , Zuo Quan Xu , Harry Zheng

Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout…

Optimization and Control · Mathematics 2019-12-30 Julien Claisse , Zhenjie Ren , Xiaolu Tan

This paper studies the linear-quadratic (LQ) optimal control problem of a class of systems governed by the first-order hyperbolic partial differential equations (PDEs) with final state constraints. The main contribution is to present the…

Optimization and Control · Mathematics 2024-11-25 Xiaomin Xue , Juanjuan Xu , Huanshui Zhang , Long Hu

We consider a class of non-cooperative N-player non-zero-sum stochastic differential games with singular controls, in which each player can affect a linear stochastic differential equation in order to minimize a cost functional which is…

Optimization and Control · Mathematics 2023-04-19 Jodi Dianetti

In this paper, we are concerned with a stochastic optimal control problem of mean-field type under partial observation, where the state equation is governed by the controlled nonlinear mean-field stochastic differential equation, moreover…

Optimization and Control · Mathematics 2016-11-15 Maonin Tang , Qingxin Meng

We study methods for solving stochastic control problems of systems of forward-backward mean-field equations with delay, in finite or infinite horizon. Necessary and sufficient maximum principles under partial information are given. The…

Optimization and Control · Mathematics 2016-10-31 Nacira Agram , Elin Engen Rose

We discuss and compare two methods of investigations for the asymptotic regime of stochastic differential games with a finite number of players as the number of players tends to the infinity. These two methods differ in the order in which…

Probability · Mathematics 2012-10-23 Rene Carmona , Francois Delarue , Aime Lachapelle

In this paper, we consider a linear-quadratic optimal control problem of mean-field stochastic differential equation with jump diffusion, which is also called as an MF-LQJ problem. Here, cost functional is allowed to be indefinite. We use…

Optimization and Control · Mathematics 2021-11-18 Guangchen Wang , Wencan Wang

In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…

Analysis of PDEs · Mathematics 2019-09-25 Jose A. Carrillo , Edgard A. Pimentel , Vardan K. Voskanyan

This paper is devoted to a global stochastic maximum principle for conditional mean-field forward-backward stochastic differential equations (FBSDEs, for short) with regime switching. The control domain is unnecessarily convex and the…

Optimization and Control · Mathematics 2022-12-06 Tao Hao , Jiaqiang Wen , Jie Xiong

In this paper, we study the linear quadratic (LQ) optimal control problem of linear systems with private input and measurement information. The main challenging lies in the unavailability of other regulators' historical input information.…

Optimization and Control · Mathematics 2023-05-29 Juanjuan Xu , Huanshui Zhang

In this paper, we first address a linear quadratic mean-field game problem with a leader-follower structure. By adopting a Riccati-type approach, we show how one can obtain a state-feedback representation of the pairs of strategies which…

Systems and Control · Electrical Eng. & Systems 2023-02-21 Samir Aberkane , Vasile Dragan

We propose a single-level numerical approach to solve Stackelberg mean field game (MFG) problems. In Stackelberg MFG, an infinite population of agents play a non-cooperative game and choose their controls to optimize their individual…

Optimization and Control · Mathematics 2024-04-24 Gokce Dayanikli , Mathieu Lauriere

This paper studies the limits of empirical means of open-loop Nash equilibria of linear-quadratic stochastic differential games as the number of players goes to infinity, when the corresponding mean field game is of potential type and may…

Probability · Mathematics 2026-02-27 Alekos Cecchin , Jodi Dianetti