相关论文: Accelerated Multiple Wasserstein Gradient Flows fo…

This paper delves into the investigation of a distributed aggregative optimization problem within a network. In this scenario, each agent possesses its own local cost function, which relies not only on the local state variable but also on…

This paper presents a theoretical framework for the design and analysis of gradient descent-based algorithms for coverage control tasks involving robot swarms. We adopt a multiscale approach to analysis and design to ensure consistency of…

Due to the high communication cost in distributed and federated learning problems, methods relying on compression of communicated messages are becoming increasingly popular. While in other contexts the best performing gradient-type methods…

We propose an algorithm for distributed optimization over time-varying communication networks. Our algorithm uses an optimized ratio between the number of rounds of communication and gradient evaluations to achieve fast convergence. The…

We study estimation problems in safety-critical applications with streaming data. Since estimation problems can be posed as optimization problems in the probability space, we devise a stochastic projected Wasserstein gradient flow that…

We investigate a stochastic program with expected value constraints, addressing the problem in a general context through Distributionally Robust Optimization (DRO) approach using Wasserstein distances, where the ambiguity set depends on the…

Score-based diffusion models have emerged as powerful tools in generative modeling, yet their theoretical foundations remain underexplored. In this work, we focus on the Wasserstein convergence analysis of score-based diffusion models.…

We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…

Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study…

Optimal Transport (OT) has attracted significant interest in the machine learning community, not only for its ability to define meaningful distances between probability distributions -- such as the Wasserstein distance -- but also for its…

Distributed optimization advances centralized machine learning methods by enabling parallel and decentralized learning processes over a network of computing nodes. This work provides an accelerated consensus-based distributed algorithm for…

Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction…

We study the contraction in Wasserstein distance of the coordinate ascent variational inference algorithm. This is shown to hold under a transport-information inequality at the fixed points and a functional smoothness condition. The results…

This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…

We present a method for solving general nonconvex-strongly-convex bilevel optimization problems. Our method -- the \emph{Restarted Accelerated HyperGradient Descent} (\texttt{RAHGD}) method -- finds an $\epsilon$-first-order stationary…

We study the Hamiltonian flow for optimization (HF-opt), which simulates the Hamiltonian dynamics for some integration time and resets the velocity to $0$ to decrease the objective function; this is the optimization analogue of the…

We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with…

We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…

We consider distributed optimization over networks where each agent is associated with a smooth and strongly convex local objective function. We assume that the agents only have access to unbiased estimators of the gradient of their…

Nonconvex and nonsmooth optimization problems are important and challenging for statistics and machine learning. In this paper, we propose Projected Proximal Gradient Descent (PPGD) which solves a class of nonconvex and nonsmooth…