30 citations · 119 across the 28 of their papers we have counts for
32 papers
Self-fictitious-play for Potential Monotone Ergodic Mean-field Games
Yupeng Bai, Mathieu Laurière, Zhenjie Ren +1
We investigate long-time learning in ergodic, potential, monotone mean-field games (MFGs) via a self-fictitious-play (SFP) dynamics coupling an optimally controlled diffusion with…
Continuous-time q-learning for mean-field control with common noise, part-II: q-learning algorithms
Zhenjie Ren, Xiaoli Wei, Xiang Yu +1
This paper is a continuation work of Ren et al. (2026) aiming to further devise q-learning algorithms for mean-field control (MFC) with controlled common noise. Based on the relaxe…
Continuous-time q-learning for mean-field control with common noise, part-I: Theoretical foundations
Zhenjie Ren, Xiaoli Wei, Xiang Yu +1
This paper investigates the continuous-time counterpart of the Q-function for entropy-regularized mean-field control (MFC) with controlled common noise, coined as q-function by Jia…
Quantitative weak propagation of chaos for McKean--Vlasov branching diffusion processes
Wenjing Cao, Zhenjie Ren, Xiaolu Tan
We study in this paper the weak propagation of chaos for McKean--Vlasov diffusions with branching, whose induced marginal measures are nonnegative finite measures but not necessary…
Dimension-free error estimate for diffusion model and optimal scheduling
Valentin de Bortoli, Romuald Elie, Anna Kazeykina +2
Diffusion generative models have emerged as powerful tools for producing synthetic data from an empirically observed distribution. A common approach involves simulating the time-re…
Uniform-in-time propagation of chaos for kinetic mean field Langevin dynamics
Fan Chen, Yiqing Lin, Zhenjie Ren +1
We study the kinetic mean field Langevin dynamics under the functional convexity assumption of the mean field energy functional. Using hypocoercivity, we first establish the expone…
Mean Field Optimization Problem Regularized by Fisher Information
Julien Claisse, Giovanni Conforti, Zhenjie Ren +1
Recently there is a rising interest in the research of mean field optimization, in particular because of its role in analyzing the training of neural networks. In this paper by add…
Uniform-in-time propagation of chaos for mean field Langevin dynamics
Fan Chen, Zhenjie Ren, Songbo Wang
We study the mean field Langevin dynamics and the associated particle system. By assuming the functional convexity of the energy, we obtain the -convergence of the marginal di…
Entropic optimal planning for path-dependent mean field games
Zhenjie Ren, Xiaolu Tan, Nizar Touzi +1
In the context of mean field games, with possible control of the diffusion coefficient, we consider a path-dependent version of the planning problem introduced by P.L. Lions: given…
Entropic Fictitious Play for Mean Field Optimization Problem
Fan Chen, Zhenjie Ren, Songbo Wang
We study two-layer neural networks in the mean field limit, where the number of neurons tends to infinity. In this regime, the optimization over the neuron parameters becomes the o…
On path-dependent multidimensional forward-backward SDEs
Kaitong Hu, Zhenjie Ren, Nizar Touzi
This paper extends the results of Ma, Wu, Zhang, Zhang [11] to the context of path-dependent multidimensional forward-backward stochastic differential equations (FBSDE). By path-de…
Entropic turnpike estimates for the kinetic Schrödinger problem
Alberto Chiarini, Giovanni Conforti, Giacomo Greco +1
We investigate the kinetic Schrödinger problem, obtained considering Langevin dynamics instead of Brownian motion in Schrödinger's thought experiment. Under a quasilinearity assump…
Ergodicity of the underdamped mean-field Langevin dynamics
Anna Kazeykina, Zhenjie Ren, Xiaolu Tan +1
We study the long time behavior of an underdamped mean-field Langevin (MFL) equation, and provide a general convergence as well as an exponential convergence rate result under diff…
Game on Random Environment, Mean-field Langevin System and Neural Networks
Giovanni Conforti, Anna Kazeykina, Zhenjie Ren
In this paper we study a type of games regularized by the relative entropy, where the players' strategies are coupled through a random environment variable. Besides the existence a…
Random horizon principal-agent problems
Yiqing Lin, Zhenjie Ren, Nizar Touzi +1
We consider a general formulation of the random horizon Principal-Agent problem with a continuous payment and a lump-sum payment at termination. In the European version of the prob…
Mean Field Games with Branching
Julien Claisse, Zhenjie Ren, Xiaolu Tan
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 set…
Continuous-Time Principal-Agent Problem in Degenerate Systems
Kaitong Hu, Zhenjie Ren, Nizar Touzi
In this paper we present a variational calculus approach to Principal-Agent problem with a lump-sum payment on finite horizon in degenerate stochastic systems, such as filtered par…
Mean-field Langevin System, Optimal Control and Deep Neural Networks
Kaitong Hu, Anna Kazeykina, Zhenjie Ren
In this paper, we study a regularised relaxed optimal control problem and, in particular, we are concerned with the case where the control variable is of large dimension. We introd…
Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks
Kaitong Hu, Zhenjie Ren, David Siska +1
Our work is motivated by a desire to study the theoretical underpinning for the convergence of stochastic gradient type algorithms widely used for non-convex learning tasks such as…
Principal-agent problem with multiple principals
Kaitong Hu, Zhenjie Ren, Junjian Yang
We consider a moral hazard problem with multiple principals in a continuous-time model. The agent can only work exclusively for one principal at a given time, so faces an optimal s…
Nonlinear predictable representation and -solutions of backward SDEs and second-order backward SDEs
Zhenjie Ren, Nizar Touzi, Junjian Yang
The theory of backward SDEs extends the predictable representation property of Brownian motion to the nonlinear framework, thus providing a path-dependent analog of fully nonlinear…
Viscosity solutions of path-dependent PDEs with randomized time
Zhenjie Ren, Mauro Rosestolato
We introduce a new definition of viscosity solution to path-dependent partial differential equations, which is a slight modification of the definition introduced in [8]. With the n…
Second order backward SDE with random terminal time
Yiqing Lin, Zhenjie Ren, Nizar Touzi +1
Backward stochastic differential equations extend the martingale representation theorem to the nonlinear setting. This can be seen as path-dependent counterpart of the extension fr…
Principal-Agent Problem with Common Agency without Communication
Thibaut Mastrolia, Zhenjie Ren
In this paper, we consider a problem of contract theory in which several Principals hire a common Agent and we study the model in the continuous time setting. We show that optimal…