scholarly journals Unified reinforcement Q-learning for mean field game and control problems

2022 ◽  
Author(s):  
Andrea Angiuli ◽  
Jean-Pierre Fouque ◽  
Mathieu Laurière
Keyword(s):  
Mean Field ◽  
Control Problems ◽  
Mean Field Game ◽  
Q Learning ◽  
And Control

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Parameter Normalization in Multibody Dynamics

2008 ◽  
Author(s):  
Saeed Ebrahimi ◽  
Jo´zsef Ko¨vecses
Keyword(s):  
Parameter Estimation ◽  
Multibody Dynamics ◽  
Eigenvalue Problems ◽  
Physical Structure ◽  
Control Problems ◽  
Inertial Parameters ◽  
Parametric Studies ◽  
Novel Concept ◽  
And Control

In this paper, we introduce a novel concept for parametric studies in multibody dynamics. This is based on a technique that makes it possible to perform a natural normalization of the dynamics in terms of inertial parameters. This normalization technique rises out from the underlying physical structure of the system, which is mathematically expressed in the form of eigenvalue problems. It leads to the introduction of the concept of dimensionless inertial parameters. This, in turn, makes the decomposition of the array of parameters possible for studying design and control problems where parameter estimation and sensitivity is of importance.

scholarly journals A MEAN FIELD GAME ANALYSIS OF SIR DYNAMICS WITH VACCINATION

2020 ◽  
pp. 1-18
Author(s):  
Josu Doncel ◽  
Nicolas Gast ◽  
Bruno Gaujal
Keyword(s):  
Mean Field ◽  
Vaccination Strategy ◽  
Game Analysis ◽  
Total Cost ◽  
Mean Field Game ◽  
Vaccination Behavior ◽  
Switching Curve ◽  
The One ◽  
The Cost ◽  
Vaccination Period

We analyze a mean field game model of SIR dynamics (Susceptible, Infected, and Recovered) where players choose when to vaccinate. We show that this game admits a unique mean field equilibrium (MFE) that consists in vaccinating at a maximal rate until a given time and then not vaccinating. The vaccination strategy that minimizes the total cost has the same structure as the MFE. We prove that the vaccination period of the MFE is always smaller than the one minimizing the total cost. This implies that, to encourage optimal vaccination behavior, vaccination should always be subsidized. Finally, we provide numerical experiments to study the convergence of the equilibrium when the system is composed by a finite number of agents ( $N$ ) to the MFE. These experiments show that the convergence rate of the cost is $1/N$ and the convergence of the switching curve is monotone.

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