10 citations · 20 across the 15 of their papers we have counts for
17 papers
A two-scale approach for sampling local free energy minimisers
Antoine Leclerc, Pierre Monmarché
When a free energy admits several local minimisers, the associated mean-field particle system exhibits a metastable behavior, undergoing random transitions between these minimisers…
Equivalence between -particle log-Sobolev inequalities and non-linear Łojasiewicz inequalities for a class of mean field systems
Pierre Monmarché
The convergence rate of a free energy Wasserstein gradient flow is quantified by its so-called Polyak-Lojasiewicz (PL) constant , which relates the objective function to its dis…
Local exponential stability of mean-field Langevin descent-ascent and associated particle system
Geuntaek Seo, Minseop Shin, Pierre Monmarché +1
We study the mean-field Langevin descent-ascent (MFL-DA), a coupled optimization dynamics on the space of probability measures for entropically regularized two-player zero-sum game…
Free energy Wasserstein gradient flow and their particle counterparts: toy model, (degenerate) PL inequalities and exit times
Pierre Monmarché
In finite dimension, the long-time and metastable behavior of a gradient flow perturbated by a small Brownian noise is well understood. A similar situation arises when a Wasserstei…
Exponential Ergodicity in Relative Entropy and -Wasserstein Distance for non-equilibrium partially dissipative Kinetic SDEs
Xing Huang, Eva Kopfer, Pierre Monmarché +1
In this paper, we derive exponential ergodicity in relative entropy for general kinetic SDEs under a partially dissipative condition. It covers non-equilibrium situations where the…
Convergence of Time-Averaged Mean Field Gradient Descent Dynamics for Continuous Multi-Player Zero-Sum Games
Yulong Lu, Pierre Monmarché
The approximation of mixed Nash equilibria (MNE) for zero-sum games with mean-field interacting players has recently raised much interest in machine learning. In this paper we prop…
Stochastic moments dynamics: a flexible finite-dimensional random perturbation of Wasserstein gradient descent
Pierre Germain, Pierre Monmarché
For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of differe…
Non-asymptotic entropic bounds for non-linear kinetic Langevin sampler with second-order splitting scheme
Pierre Monmarché, Katharina Schuh
The problem of sampling according to the probability distribution minimizing a given free energy, using interacting particles unadjusted kinetic Langevin Monte Carlo, is addressed.…
Uniform log-Sobolev inequalities for mean field particles beyond flat-convexity
Pierre Monmarché
In the nice recent work [48], S. Wang established uniform log-Sobolev inequalities for mean field particles when the energy is flat convex. In this note we comment how to extend hi…
Local convergence rates for Wasserstein gradient flows and McKean-Vlasov equations with multiple stationary solutions
Pierre Monmarché, Julien Reygner
Non-linear versions of log-Sobolev inequalities, that link a free energy to its dissipation along the corresponding Wasserstein gradient flow (i.e. corresponds to Polyak-Lojasiewic…
Time-uniform log-Sobolev inequalities and applications to propagation of chaos
Pierre Monmarché, Zhenjie Ren, Songbo Wang
Time-uniform log-Sobolev inequalities (LSI) satisfied by solutions of semi-linear mean-field equations have recently appeared to be a key tool to obtain time-uniform propagation of…
-Wasserstein contraction for Euler schemes of elliptic diffusions and interacting particle systems
Linshan Liu, Mateusz B. Majka, Pierre Monmarché
We show the -Wasserstein contraction for the transition kernel of a discretised diffusion process, under a contractivity at infinity condition on the drift and a sufficiently…
Asymptotic expansion of the invariant measurefor Markov-modulated ODEs at high frequency
Pierre Monmarché, Edouard Strickler
We consider time-inhomogeneous ODEs whose parameters are governed by an underlying ergodic Markov process. When this underlying process is accelerated by a factor $\varepsilon^{-1}…
Second order quantitative bounds for unadjusted generalized Hamiltonian Monte Carlo
Evan Camrud, Alain Durmus, Pierre Monmarché +1
This paper provides a convergence analysis for generalized Hamiltonian Monte Carlo samplers, a family of Markov Chain Monte Carlo methods based on leapfrog integration of Hamiltoni…
Piecewise deterministic sampling with splitting schemes
Andrea Bertazzi, Paul Dobson, Pierre Monmarché
We introduce Markov chain Monte Carlo (MCMC) algorithms based on numerical approximations of piecewise-deterministic Markov processes obtained with the framework of splitting schem…
Wasserstein contraction and Poincaré inequalities for elliptic diffusions at high temperature
Pierre Monmarché
We consider elliptic diffusion processes on . Assuming that the drift contracts distances outside a compact set, we prove that, at a sufficiently high temperature, the…
High-dimensional MCMC with a standard splitting scheme for the underdamped Langevin diffusion
Pierre Monmarché
The efficiency of a Markov sampler based on the underdamped Langevin diffusion is studied for high dimensional targets with convex and smooth potentials. We consider a classical se…