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We propose a relative entropy gradient sampler (REGS) for sampling from unnormalized distributions. REGS is a particle method that seeks a sequence of simple nonlinear transforms iteratively pushing the initial samples from a reference…
The so-called JKO scheme, named after Jordan, Kinderlehrer and Otto, provides a variational way to construct discrete time approximations of certain partial differential equations (PDEs) appearing as gradient flows in the space of…
The proximal bundle method (PBM) is a fundamental and computationally effective algorithm for solving nonsmooth optimization problems. In this paper, we present the first variant of the PBM for smooth objectives, achieving an accelerated…
In this paper, we focus on non-asymptotic bounds related to the Euler scheme of an ergodic diffusion with a possibly multiplicative diffusion term (non-constant diffusion coefficient). More precisely, the objective of this paper is to…
Wasserstein barycenter is the centroid of a collection of discrete probability distributions which minimizes the average of the $\ell_2$-Wasserstein distance. This paper focuses on the computation of Wasserstein barycenters under the case…
Construction of ambiguity set in robust optimization relies on the choice of divergences between probability distributions. In distribution learning, choosing appropriate probability distributions based on observed data is critical for…
In this paper, we analyse a proximal method based on the idea of forward-backward splitting for sampling from distributions with densities that are not necessarily smooth. In particular, we study the non-asymptotic properties of the…
Focus of this work is solving a non-smooth constraint minimization problem by a primal-dual splitting algorithm involving proximity operators. The problem is penalized by the Bregman divergence associated with the non-smooth total variation…
This work studies the convergence and finite sample approximations of entropic regularized Wasserstein distances in the Hilbert space setting. Our first main result is that for Gaussian measures on an infinite-dimensional Hilbert space,…
Variational inference, such as the mean-field (MF) approximation, requires certain conjugacy structures for efficient computation. These can impose unnecessary restrictions on the viable prior distribution family and further constraints on…
In this paper, we present a new policy gradient (PG) methods, namely the block policy mirror descent (BPMD) method for solving a class of regularized reinforcement learning (RL) problems with (strongly)-convex regularizers. Compared to the…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
The analysis of structure-preserving numerical methods for the Poisson--Nernst--Planck (PNP) system has attracted growing interests in recent years. In this work, we provide an optimal rate convergence analysis and error estimate for finite…
Variational problems that involve Wasserstein distances have been recently proposed to summarize and learn from probability measures. Despite being conceptually simple, such problems are computationally challenging because they involve…
In this work, we propose a sparse transformer architecture that incorporates prior information about the underlying data distribution directly into the transformer structure of the neural network. The design of the model is motivated by a…
Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target…
Combining the classical theory of optimal transport with modern operator splitting techniques, we develop a new numerical method for nonlinear, nonlocal partial differential equations, arising in models of porous media, materials science,…
In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly…
We consider the population Wasserstein barycenter problem for random probability measures supported on a finite set of points and generated by an online stream of data. This leads to a complicated stochastic optimization problem where the…
We study a general formulation of regularized Wasserstein barycenters that enjoys favorable regularity, approximation, stability and (grid-free) optimization properties. This barycenter is defined as the unique probability measure that…