10 papers
A Stochastic Optimization Approach to Control-Affine Optimal Control Problems
Eloïse Berthier, Ziad Kobeissi, Francis Bach
We consider control-affine optimal control problems on the torus, where the dynamics and cost functions are only accessed through samples. Starting from a weak formulation of such…
Fast and Robust Convergence Rate for TD(0) with Linear Function Approximation, Universal Learning Steps and I.I.D. Samples
Ziad Kobeissi, Éloïse Berthier
In this paper, we study the finite-time behavior of the TD(0) temporal-difference method with linear function approximation (LFA). We consider on-policy independent and identically…
Mean-field games for harvesting problems: Uniqueness, long-time behaviour and weak KAM theory
Ziad Kobeissi, Idriss Mazari-Fouquer, Domènec Ruiz-Balet
The goal of this paper is to study a Mean Field Game (MFG) system stemming from the harvesting of resources. Modelling the latter through a reaction-diffusion equation and the harv…
The tragedy of the commons: A Mean-Field Game approach to the reversal of travelling waves
Ziad Kobeissi, Idriss Mazari-Fouquer, Domenec Ruiz-Balet
The goal of this paper is to investigate an instance of the tragedy of the commons in spatially distributed harvesting games. The model we choose is that of a fishes' population th…
A Non-asymptotic Analysis of Non-parametric Temporal-Difference Learning
Eloïse Berthier, Ziad Kobeissi, Francis Bach
Temporal-difference learning is a popular algorithm for policy evaluation. In this paper, we study the convergence of the regularized non-parametric TD(0) algorithm, in both the in…
Temporal Difference Learning with Continuous Time and State in the Stochastic Setting
Ziad Kobeissi, Francis Bach
We consider the problem of continuous-time policy evaluation. This consists in learning through observations the value function associated with an uncontrolled continuous-time stoc…
Mean Field Games with monotonous interactions through the law of states and controls of the agents
Z Kobeissi
We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian beha…
Mean Field Games of Controls: Finite Difference Approximations
Y Achdou, Z Kobeissi
We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her…
On Classical Solutions to the Mean Field Game System of Controls
Z Kobeissi
In this paper, we consider a class of mean field games in which the optimal strategy of a representative agent depends on the statistical distribution of the states and controls. W…
On the implementation of a primal-dual algorithm for second order time-dependent mean field games with local couplings
Luis Briceño-Arias, Dante Kalise, Ziad Kobeissi +3
We study a numerical approximation of a time-dependent Mean Field Game (MFG) system with local couplings. The discretization we consider stems from a variational approach described…