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A dynamic mean field theory is developed for finite state and action Bayesian reinforcement learning in the large state space limit. In an analogy with statistical physics, the Bellman equation is studied as a disordered dynamical system;…

Machine Learning · Statistics 2023-07-13 George Stamatescu

In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…

Optimization and Control · Mathematics 2025-12-05 P. Jameson Graber , Kyle Rosengartner

We consider a classical finite horizon optimal control problem for continuous-time pure jump Markov processes described by means of a rate transition measure depending on a control parameter and controlled by a feedback law. For this class…

Probability · Mathematics 2015-01-20 Elena Bandini , Marco Fuhrman

This paper investigates the optimal harvesting strategy for a single species living in random environments whose growth is given by a regime-switching diffusion. Harvesting acts as a (stochastic) control on the size of the population. The…

Optimization and Control · Mathematics 2016-08-02 Qingshuo Song , Richard Stockbridge , Chao Zhu

We consider a class of stochastic control problems which has been widely used in optimal foraging theory. The state processes have two distinct dynamics, characterized by two pairs of drift and diffusion coefficients, depending on whether…

Optimization and Control · Mathematics 2024-04-12 Zengjing Chen , Panyu Wu , Xiaowen Zhou

Mean field games and controls involve guiding the behavior of large populations of interacting agents, where each individual's influence on the group is negligible but collectively impacts overall dynamics. Hybrid systems integrate…

Optimization and Control · Mathematics 2024-12-17 Tejaswi K. C. , Taeyoung Lee

Liquid droplet dynamics are widely used in biological and engineering applications, which contain complex interfacial instabilities and pattern formation such as droplet merging, splitting, and transport. This paper studies a class of mean…

Optimization and Control · Mathematics 2024-10-10 Guosheng Fu , Hangjie Ji , Will Pazner , Wuchen Li

In this paper we study a class of stochastic control problems in which the control of the jump size is essential. Such a model is a generalized version for various applied problems ranging from optimal reinsurance selections for general…

Probability · Mathematics 2008-04-04 Rainer Buckdahn , Jin Ma , Catherine Rainer

We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton-Jacobi equations (HJ), prove the comparison principle and that…

Analysis of PDEs · Mathematics 2020-02-25 Manh-Khang Dao , Boualem Djehiche

The paper is concerned with the study of a control system consisting of one major agent and many identical minor agents in the limit case when the number of agents tends to infinity. To study the limiting system we use the mean field…

Optimization and Control · Mathematics 2022-12-13 Yurii Averboukh

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by $L^1$-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic…

Optimization and Control · Mathematics 2021-01-27 J. Baumeister , A. Leitao , G. N. Silva

We provide some criteria on the stability of regime-switching diffusion processes. Both the state-independent and state-dependent regime-switching diffusion processes with switching in a finite state space and an infinite countable state…

Probability · Mathematics 2015-03-10 Jinghai Shao , Fubao Xi

Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in $\mathbf {R}^m$ in the presence of a random environment and…

Probability · Mathematics 2014-07-03 Eric Luçon , Wilhelm Stannat

This paper deals with a stochastic recursive optimal control problem, where the diffusion coefficient depends on the control variable and the control domain is not necessarily convex. We focus on the connection between the general maximum…

Optimization and Control · Mathematics 2016-12-21 Tianyang Nie , Jingtao Shi , Zhen Wu

In this paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming…

Probability · Mathematics 2013-01-03 Shaolin Ji , Shuzhen Yang

This paper develops a non-asymptotic, local approach to quantitative propagation of chaos for a wide class of mean field diffusive dynamics. For a system of $n$ interacting particles, the relative entropy between the marginal law of $k$…

Probability · Mathematics 2023-05-31 Daniel Lacker

We consider a time-consistent mean-variance portfolio selection problem of an insurer and allow for the incorporation of basis (mortality) risk. The optimal solution is identified with a Nash subgame perfect equilibrium. We characterize an…

Portfolio Management · Quantitative Finance 2019-08-16 Frank Bosserhoff , Mitja Stadje

In this paper we consider a mean field approach to modeling the agents flow over a transportation network. In particular, beside a standard framework of mean field games, with controlled dynamics by the agents and costs mass-distribution…

Optimization and Control · Mathematics 2020-06-18 Fabio Bagagiolo , Rosario Maggistro , Raffaele Pesenti

We investigate the global numerical approximation of a class of extended mean field control problems (MFC), where the dynamics and costs depend on the joint distribution of the state and the control. We propose a framework to approximate…

Optimization and Control · Mathematics 2026-03-23 Athena Picarelli , Marco Scaratti , Jonathan Tam

This paper is devoted to the stochastic optimal control problem of ordinary differential equations allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases, the value function turns…

Optimization and Control · Mathematics 2021-10-25 Jinniao Qiu