8 papers
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…
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…
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…
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…
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…