相关论文: Distributed Optimization with Quantization for Com…

Learning generative models is challenging for a network edge node with limited data and computing power. Since tasks in similar environments share model similarity, it is plausible to leverage pre-trained generative models from the cloud or…

We propose a distributionally robust classification model with a fairness constraint that encourages the classifier to be fair in view of the equality of opportunity criterion. We use a type-$\infty$ Wasserstein ambiguity set centered at…

A variety of problems in distributed control involve a networked system of autonomous agents cooperating to carry out some complex task in a decentralized fashion, e.g., orienting a flock of drones, or aggregating data from a network of…

Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…

Let $\mathcal{P}_{2,ac}$ be the set of Borel probabilities on $\mathbb{R}^d$ with finite second moment and absolutely continuous with respect to Lebesgue measure. We consider the problem of finding the barycenter (or Fr\'echet mean) of a…

The notion of entropy-regularized optimal transport, also known as Sinkhorn divergence, has recently gained popularity in machine learning and statistics, as it makes feasible the use of smoothed optimal transportation distances for data…

Communication efficient distributed mean estimation is an important primitive that arises in many distributed learning and optimization scenarios such as federated learning. Without any probabilistic assumptions on the underlying data, we…

Computational implementation of optimal transport barycenters for a set of target probability measures requires a form of approximation, a widespread solution being empirical approximation of measures. We provide an $O(\sqrt{N/n})$…

This paper develops distributed synchronous and asynchronous algorithms for the large-scale semi-definite programming with diagonal constraints, which has wide applications in combination optimization, image processing and community…

The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…

This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of…

We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where…

Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…

A data-driven formulation of the optimal transport problem is presented and solved using adaptively refined meshes to decompose the problem into a sequence of finite linear programming problems. Both the marginal distributions and their…

We study sparse optimal control of a non-local continuity equation, where the goal is to steer a distribution via finitely many controllable agents or actuators. This model arises naturally in mean-field multi-agent systems and takes the…

Hyperspectral images capture vast amounts of high-dimensional spectral information about a scene, making labeling an intensive task that is resistant to out-of-the-box statistical methods. Unsupervised learning of clusters allows for…

Variational inference (VI) can be cast as an optimization problem in which the variational parameters are tuned to closely align a variational distribution with the true posterior. The optimization task can be approached through vanilla…