Related papers: Fixed-Point Neural Optimal Transport without Impli…
We provide a framework for computing the exact worst-case performance of any algorithm belonging to a broad class of oracle-based first-order methods for composite convex optimization, including those performing explicit, projected,…
Optimal Transport (OT) problems are a cornerstone of many applications, but solving them is computationally expensive. To address this problem, we propose UNOT (Universal Neural Optimal Transport), a novel framework capable of accurately…
We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT…
This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…
We present a self-contained analysis of a particular family of metrics over the set of non-negative integers. We show that these metrics, which are defined through a nested sequence of optimal transport problems, provide tight estimates for…
Recent studies have demonstrated the vulnerability of deep convolutional neural networks against adversarial examples. Inspired by the observation that the intrinsic dimension of image data is much smaller than its pixel space dimension and…
We propose a \textbf{uni}fied \textbf{f}ramework for \textbf{i}mplicit \textbf{ge}nerative \textbf{m}odeling (UnifiGem) with theoretical guarantees by integrating approaches from optimal transport, numerical ODE, density-ratio…
In this paper, we study the decentralized optimization problem of minimizing a finite sum of continuously differentiable and possibly nonconvex functions over a fixed-connected undirected network. We propose a unified decentralized…
Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…
Neural networks trained with standard objectives exhibit behaviors characteristic of probabilistic inference: soft clustering, prototype specialization, and Bayesian uncertainty tracking. These phenomena appear across architectures -- in…
To improve the performance of classical generative adversarial network (GAN), Wasserstein generative adversarial networks (W-GAN) was developed as a Kantorovich dual formulation of the optimal transport (OT) problem using Wasserstein-1…
Optimal transport is a powerful framework for the efficient allocation of resources between sources and targets. However, traditional models often struggle to scale effectively in the presence of large and heterogeneous populations. In this…
We provide a framework to approximate the 2-Wasserstein distance and the optimal transport map, amenable to efficient training as well as statistical and geometric analysis. With the quadratic cost and considering the Kantorovich dual form…
Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…
This paper develops a unified distributed method for solving two classes of constrained networked optimization problems, i.e., optimal consensus problem and resource allocation problem with non-identical set constraints. We first transform…
This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…
We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans…
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…
We consider a generic decentralized constrained optimization problem over static, directed communication networks, where each agent has exclusive access to only one convex, differentiable, local objective term and one convex constraint set.…
This paper connects discrete optimal transport to a certain class of multi-objective optimization problems. In both settings, the decision variables can be organized into a matrix. In the multi-objective problem, the notion of Pareto…