60 citations · 133 across the 19 of their papers we have counts for
25 papers
Reproducing kernel approach to linear quadratic mean field control problems
Pierre-Cyril Aubin-Frankowski, Alain Bensoussan
Mean-field control problems have received continuous interest over the last decade. Despite being more intricate than in classical optimal control, the linear-quadratic setting can…
Alternating minimization for simultaneous estimation of a latent variable and identification of a linear continuous-time dynamic system
Pierre-Cyril Aubin-Frankowski, Alain Bensoussan, S. Joe Qin
We propose an optimization formulation for the simultaneous estimation of a latent variable and the identification of a linear continuous-time dynamic system, given a single input-…
Mean Field Type Control Problems, Some Hilbert-space-valued FBSDEs, and Related Equations
Alain Bensoussan, Ho Man Tai, Sheung Chi Phillip Yam
In this article, we provide an original systematic global-in-time analysis of mean field type control problems on with generic cost functionals by the modified appro…
A Theory of First Order Mean Field Type Control Problems and their Equations
Alain Bensoussan, Tak Kwong Wong, Sheung Chi Phillip Yam +1
In this article, by using several new crucial {\it a priori} estimates which are still absent in the literature, we provide a comprehensive resolution of the first order generic me…
A Deep Learning Approximation of Non-Stationary Solutions to Wave Kinetic Equations
Steven Walton, Minh-Binh Tran, Alain Bensoussan
We present a deep learning approximation, stochastic optimization based, method for wave kinetic equations. To build confidence in our approach, we apply the method to a Smoluchows…
The reproducing kernel Hilbert spaces underlying linear SDE Estimation, Kalman filtering and their relation to optimal control
Pierre-Cyril Aubin-Frankowski, Alain Bensoussan
It is often said that control and estimation problems are in duality. Recently, in (Aubin-Frankowski,2021), we found new reproducing kernels in Linear-Quadratic optimal control by…
Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems
Pierre-Cyril Aubin-Frankowski, Alain Bensoussan
The Linear Quadratic Regulator (LQR), which is arguably the most classical problem in control theory, was recently related to kernel methods in (Aubin-Frankowski, SICON, 2021) for…
Control in Hilbert Space and First Order Mean Field Type Problem
Alain Bensoussan, Henry Hang Cheung, Sheung Chi Phillip Yam
We extend the work \cite{bensoussan2019control} by two of the coauthors, which dealt with a deterministic control problem for which the Hilbert space could be generic and investiga…
Value-Gradient based Formulation of Optimal Control Problem and Machine Learning Algorithm
Alain Bensoussan, Jiayue Han, Sheung Chi Phillip Yam +1
Optimal control problem is typically solved by first finding the value function through Hamilton-Jacobi equation (HJE) and then taking the minimizer of the Hamiltonian to obtain th…
Machine Learning and Control Theory
Alain Bensoussan, Yiqun Li, Dinh Phan Cao Nguyen +3
We survey in this article the connections between Machine Learning and Control Theory. Control Theory provide useful concepts and tools for Machine Learning. Conversely Machine Lea…
Identification of linear dynamical systems and machine learning
Alain Bensoussan, Fatih Gelir, Viswanath Ramakrishna +1
The topic of identification of dynamic systems, has been at the core of modern control , following the fundamental works of Kalman. Realization Theory has been one of the major out…
Control on Hilbert Spaces and Application to Some Mean Field Type Control Problems
Alain Bensoussan, P. Jameson Graber, Sheung Chi Phillip Yam
We propose a new approach to studying classical solutions of the Bellman equation and Master equation for mean field type control problems, using a novel form of the "lifting" idea…
Mean Field approach to stochastic control with partial information
Alain Bensoussan, Sheung Chi Phillip Yam
The classical stochastic control problem under partial information can be formulated as a control problem for Zakai equation, whose solution is the unnormalized conditional probabi…
Stochastic Control on Space of Random Variables
Alain Bensoussan, P. Jameson Graber, S. C. P. Yam
By extending \cite{bensoussan2015control}, we implement the proposal of Lions \cite{lions14} on studying mean field games and their master equations via certain control problems on…
Mean Field Control and Mean Field Game Models with Several Populations
Alain Bensoussan, Tao Huang, Mathieu Laurière
In this paper, we investigate the interaction of two populations with a large number of indistinguishable agents. The problem consists in two levels: the interaction between agents…
Optimal periodic replenishment policies for spectrally positive Lévy demand processes
José-Luis Pérez, Kazutoshi Yamazaki, Alain Bensoussan
We consider a version of the stochastic inventory control problem for a spectrally positive Lévy demand process, in which the inventory can only be replenished at independent expon…
Bellman systems with mean field dependent dynamics
Alain Bensoussan, Miroslav Bulíček, Jens Frehse
We deal with nonlinear elliptic and parabolic systems that are the Bellman like systems associated to stochastic differential games with mean field dependent dynamics. The key nove…
Risk-Sensitive Mean-Field-Type Control
Alain Bensoussan, Boualem Djehiche, Hamidou Tembine +1
We study risk-sensitive optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law a…
Mean-field-game model for Botnet defense in Cyber-security
Vassili Kolokoltsov, Alain Bensoussan
We initiate the analysis of the response of computer owners to various offers of defence systems against a cyber-hacker (for instance, a botnet attack), as a stochastic game of a l…
On The Interpretation Of The Master Equation
Alain Bensoussan, Jens Frehse, Phillip Yam
Since its introduction by P.L. Lions in his lectures and seminars at the College de France, see [9], and also the very helpful notes of Cardialaguet [4] on Lions' lectures, the Mas…
Linear-Quadratic Mean Field Games
Alain Bensoussan, Joseph Sung, Phillip Yam +1
In this article, we provide a comprehensive study of the linear-quadratic mean field games via the adjoint equation approach; although the problem has been considered in the litera…
The Master Equation in Mean Field Theory
Alain Bensoussan, Jens Frehse, Phillip Yam
In his lectures at College de France, P.L. Lions introduced the concept of Master equation, see [5] for Mean Field Games. It is introduced in a heuristic fashion, from the system o…
The Maximum Principle for Global Solutions of Stochastic Stackelberg Differential Games
Alain Bensoussan, Shaokuan Chen, Suresh P. Sethi
This paper obtains the maximum principle for both stochastic (global) open-loop and stochastic (global) closed-loop Stackelberg differential games. For the closed-loop case, we use…
Degenerate Dirichlet Problems Related to the Ergodic Property of an Elasto-Plastic Oscillator Excited by a Filtered White Noise
Alain Bensoussan, Laurent Mertz
A stochastic variational inequality is proposed to model an elasto-plastic oscillator excited by a filtered white noise. We prove the ergodic properties of the process and characte…