Related papers: Dual Block Gradient Ascent for Entropically Regula…
This paper improves the state-of-the-art rate of a first-order algorithm for solving entropy regularized optimal transport. The resulting rate for approximating the optimal transport (OT) has been improved from…
We consider the entropic regularization of discretized optimal transport and propose to solve its optimality conditions via a logarithmic Newton iteration. We show a quadratic convergence rate and validate numerically that the method…
Adding entropic regularization to Optimal Transport (OT) problems has become a standard approach for designing efficient and scalable solvers. However, regularization introduces a bias from the true solution. To mitigate this bias while…
Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…
We consider the maximum-a-posteriori inference problem in discrete graphical models and study solvers based on the dual block-coordinate ascent rule. We map all existing solvers in a single framework, allowing for a better understanding of…
This paper deals with maximum entropy completion of partially specified block-circulant matrices. Since positive definite symmetric circulants happen to be covariance matrices of stationary periodic processes, in particular of stationary…
We study level set teleportation, an optimization routine which tries to accelerate gradient descent (GD) by maximizing the gradient norm over a level set of the objective. While teleportation intuitively speeds-up GD via bigger steps,…
In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…
In this paper, we first revisit the Koenker and Bassett variational approach to (univariate) quantile regression, emphasizing its link with latent factor representations and correlation maximization problems. We then review the multivariate…
This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…
We propose an efficient dual algorithm for ELP based on Fast Gradient Method. The basic idea - to solve properly regularized dual problem.
We introduce a new class of convex-regularized Optimal Transport losses, which generalizes the classical Entropy-regularization of Optimal Transport and Sinkhorn divergences, and propose a generalized Sinkhorn algorithm. Our framework…
Linear programs with quadratic regularization are attracting renewed interest due to their applications in optimal transport: unlike entropic regularization, the squared-norm penalty gives rise to sparse approximations of optimal transport…
Calculations using the (exact) fermionic functional renormalization group are usually truncated at the second order of the corresponding hierarchy of coupled ordinary differential equations. We present a method for the systematic…
Entropic optimal transport offers a computationally tractable approximation to the classical problem. In this note, we study the approximation rate of the entropic optimal transport map (in approaching the Brenier map) when the…
We study the semi-discrete formulation of one-dimensional partial optimal transport with quadratic cost, where a probability density is partially transported to a finite sum of Dirac masses of smaller total mass. This problem arises…
A quantum algorithm for simulating multidimensional scalar transport problems using a time-marching strategy is presented. A direct unitary block encoding of the explicit time-marching operator is constructed, resulting in the intrinsic…
There will be a fast-paced shift from conventional network systems to novel quantum networks that are supported by the quantum entanglement and teleportation, key technologies of the quantum era, to enable secured data transmissions in the…
Communication efficiency is a major bottleneck in the applications of distributed networks. To address the problem, the problem of quantized distributed optimization has attracted a lot of attention. However, most of the existing quantized…
In this paper, we consider continuous-time stochastic optimal control problems where the cost is evaluated through a coherent risk measure. We provide an explicit gradient descent-ascent algorithm which applies to problems subject to…