Related papers: Efficient Optimal Transport Algorithm by Accelerat…
Optimal transport has been an essential tool for reconstructing dynamics from complex data. With the increasingly available multifaceted data, a system can often be characterized across multiple spaces. Therefore, it is crucial to maintain…
The stochastic three points (STP) algorithm is a derivative-free optimization technique designed for unconstrained optimization problems in $\mathbb{R}^d$. In this paper, we analyze this algorithm for three classes of functions: smooth…
Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by…
Introduced by Beck and Teboulle, FISTA (for Fast Iterative Shrinkage-Thresholding Algorithm) is a first-order method widely used in convex optimization. Adapted from Nesterov's accelerated gradient method for convex functions, the generated…
This work considers minimizing a sum of convex functions, each with potentially different structure ranging from nonsmooth to smooth, Lipschitz to non-Lipschitz. Nesterov's universal fast gradient method provides an optimal black-box…
We consider the problem of minimizing a smooth convex function by reducing the optimization to computing the Nash equilibrium of a particular zero-sum convex-concave game. Zero-sum games can be solved using online learning dynamics, where a…
Convergence analysis of accelerated first-order methods for convex optimization problems are presented from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient flow, has…
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…
Optimal Transport (OT) offers a powerful framework for finding correspondences between distributions and addressing matching and alignment problems in various areas of computer vision, including shape analysis, image generation, and…
We propose a novel exact algorithm for the transportation problem, one of the paradigmatic network optimization problems. The algorithm, denoted Iterated Inside Out, requires in input a basic feasible solution and is composed by two main…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
Comparing time series in a principled manner requires capturing both temporal alignment and distributional similarity of features. Optimal transport (OT) has recently emerged as a powerful tool for this task, but existing OT-based…
This paper proposes a novel CTA (Combine-Then-Adapt)-based decentralized algorithm for solving convex composite optimization problems over undirected and connected networks. The local loss function in these problems contains both smooth and…
Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if…
This paper proposes an efficient numerical optimization approach for solving dynamic optimal transport (DOT) problems on general smooth surfaces, computing both the quadratic Wasserstein distance and the associated transportation path.…
The Unbalanced Optimal Transport (UOT) problem plays increasingly important roles in computational biology, computational imaging and deep learning. Scaling algorithm is widely used to solve UOT due to its convenience and good convergence…
In this paper we deal with a general second order continuous dynamical system associated to a convex minimization problem with a Fr\`echet differentiable objective function. We show that inertial algorithms, such as Nesterov's algorithm,…
Given a $d$-dimensional continuous (resp. discrete) probability distribution $\mu$ and a discrete distribution $\nu$, the semi-discrete (resp. discrete) Optimal Transport (OT) problem asks for computing a minimum-cost plan to transport mass…
A class of second-order algorithms is proposed for minimizing smooth nonconvex functions that alternates between regularized Newton and negative curvature steps in an iteration-dependent subspace. In most cases, the Hessian matrix is…
We analyze continuous optimal transport problems in the so-called Kantorovich form, where we seek a transport plan between two marginals that are probability measures on compact subsets of Euclidean space. We consider the case of…