40 citations · 69 across the 16 of their papers we have counts for
21 papers
On the computational cost of Stochastic Gradient Langevin Dynamics
Mateusz B. Majka, Tigran Nagapetyan, Łukasz Szpruch +2
Stochastic Gradient Langevin Dynamics (SGLD) reduces the cost of Langevin-based sampling by replacing full-dataset drift evaluations with mini-batch approximations, but the resulti…
On propagation of chaos for the Fisher-Rao gradient flow in entropic mean-field optimization
Petra Lazić, Linshan Liu, Mateusz B. Majka
We consider a class of optimization problems on the space of probability measures motivated by the mean-field approach to studying neural networks. Such problems can be solved by c…
Non-convex entropic mean-field optimization via Best Response flow
Razvan-Andrei Lascu, Mateusz B. Majka
We study the problem of minimizing non-convex functionals on the space of probability measures, regularized by the relative entropy (KL divergence) with respect to a fixed referenc…
Geometric ergodicity of modified Euler schemes for SDEs with super-linearity
Jianhai Bao, Mateusz B. Majka, Jian Wang
As a well-known fact, the classical Euler scheme works merely for SDEs with coefficients of linear growth. In this paper, we study a general framework of modified Euler schemes, wh…
Linear convergence of proximal descent schemes on the Wasserstein space
Razvan-Andrei Lascu, Mateusz B. Majka, David Šiška +1
We investigate proximal descent methods, inspired by the minimizing movement scheme introduced by Jordan, Kinderlehrer and Otto, for optimizing entropy-regularized functionals on t…
A Fisher-Rao gradient flow for entropic mean-field min-max games
Razvan-Andrei Lascu, Mateusz B. Majka, Łukasz Szpruch
Gradient flows play a substantial role in addressing many machine learning problems. We examine the convergence in continuous-time of a \textit{Fisher-Rao} (Mean-Field Birth-Death)…
Mirror Descent-Ascent for mean-field min-max problems
Razvan-Andrei Lascu, Mateusz B. Majka, Łukasz Szpruch
We study two variants of the mirror descent-ascent (MDA) algorithm for solving min-max problems on the space of measures: simultaneous and alternating. We work under assumptions 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…
Entropic mean-field min-max problems via Best Response flow
Razvan-Andrei Lascu, Mateusz B. Majka, Łukasz Szpruch
We investigate the convergence properties of a continuous-time optimization method, the \textit{Mean-Field Best Response} flow, for solving convex-concave min-max games with entrop…
Optimal Markovian coupling for finite activity Lévy processes
Wilfrid S. Kendall, Mateusz B. Majka, Aleksandar Mijatović
We study optimal Markovian couplings of Markov processes, where the optimality is understood in terms of minimization of concave transport costs between the time-marginal distribut…
Polyak-Łojasiewicz inequality on the space of measures and convergence of mean-field birth-death processes
Linshan Liu, Mateusz B. Majka, Łukasz Szpruch
The Polyak-Lojasiewicz inequality (PLI) in is a natural condition for proving convergence of gradient descent algorithms. In the present paper, we study an analogue…
Strict Kantorovich contractions for Markov chains and Euler schemes with general noise
Lu-Jing Huang, Mateusz B. Majka, Jian Wang
We study contractions of Markov chains on general metric spaces with respect to some carefully designed distance-like functions, which are comparable to the total variation and the…
Approximation of heavy-tailed distributions via stable-driven SDEs
Lu-Jing Huang, Mateusz B. Majka, Jian Wang
Constructions of numerous approximate sampling algorithms are based on the well-known fact that certain Gibbs measures are stationary distributions of ergodic stochastic differenti…
Multi-index Antithetic Stochastic Gradient Algorithm
Mateusz B. Majka, Marc Sabate-Vidales, Łukasz Szpruch
Stochastic Gradient Algorithms (SGAs) are ubiquitous in computational statistics, machine learning and optimisation. Recent years have brought an influx of interest in SGAs, and th…
Exponential ergodicity for SDEs and McKean-Vlasov processes with Lévy noise
Mingjie Liang, Mateusz B. Majka, Jian Wang
We study stochastic differential equations (SDEs) of McKean-Vlasov type with distribution dependent drifts and driven by pure jump Lévy processes. We prove a uniform in time propag…
Quantitative contraction rates for Markov chains on general state spaces
Andreas Eberle, Mateusz B. Majka
We investigate the problem of quantifying contraction coefficients of Markov transition kernels in Kantorovich ( Wasserstein) distances. For diffusion processes, relatively pr…
Non-asymptotic bounds for sampling algorithms without log-concavity
Mateusz B. Majka, Aleksandar Mijatović, Lukasz Szpruch
Discrete time analogues of ergodic stochastic differential equations (SDEs) are one of the most popular and flexible tools for sampling high-dimensional probability measures. Non-a…
A note on existence of global solutions and invariant measures for jump SDEs with locally one-sided Lipschitz drift
Mateusz B. Majka
We extend some methods developed by Albeverio, Brzeźniak and Wu and we show how to apply them in order to prove existence of global strong solutions of stochastic differential equa…
Transportation inequalities for non-globally dissipative SDEs with jumps via Malliavin calculus and coupling
Mateusz B. Majka
By using the mirror coupling for solutions of SDEs driven by pure jump Lévy processes, we extend some transportation and concentration inequalities, which were previously known onl…
Multilevel Monte Carlo methods for the approximation of invariant measures of stochastic differential equations
Michael B. Giles, Mateusz B. Majka, Lukasz Szpruch +2
We develop a framework that allows the use of the multi-level Monte Carlo (MLMC) methodology (Giles2015) to calculate expectations with respect to the invariant measure of an ergod…
Coupling and exponential ergodicity for stochastic differential equations driven by Lévy processes
Mateusz B. Majka
We present a novel idea for a coupling of solutions of stochastic differential equations driven by Lévy noise, inspired by some results from the optimal transportation theory. Then…