相关论文: On the convergence of the distributed proximal poi…

Important applications in robotic and sensor networks require distributed algorithms to solve the so-called relative localization problem: a node-indexed vector has to be reconstructed from measurements of differences between neighbor…

In this work, we are concerned with the decentralized optimization problem: \begin{equation*} \min_{x \in \Omega}~f(x) = \frac{1}{n} \sum_{i=1}^n f_i (x), \end{equation*} where $\Omega \subset \mathbb{R}^d$ is a convex domain and each $f_i…

This paper studies distributed resource allocation problem in multi-agent systems, where all the agents cooperatively minimize the sum of their cost functions with global resource constraints over stochastic communication networks. This…

We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To…

In this paper, we explore the two-point zeroth-order gradient estimator and identify the distribution of random perturbations that minimizes the estimator's asymptotic variance as the perturbation stepsize tends to zero. We formulate it as…

This work focuses on a class of general decentralized constraint-coupled optimization problems. We propose a novel nested primal-dual gradient algorithm (NPGA), which can achieve linear convergence under the weakest known condition, and its…

Efficient computation of min-max problems is a central question in optimization, learning, games, and controls. Arguably the most natural algorithm is gradient-descent-ascent (GDA). However, since the 1970s, conventional wisdom has argued…

In this paper, we consider a class of single-ratio fractional minimization problems, where both the numerator and denominator of the objective are convex functions satisfying positive homogeneity. Many nonsmooth optimization problems on the…

Distributed optimization and learning algorithms are designed to operate over large scale networks enabling processing of vast amounts of data effectively and efficiently. One of the main challenges for ensuring a smooth learning process in…

We propose a distributed algorithm, termed the Directed-Distributed Projected Subgradient (D-DPS), to solve a constrained optimization problem over a multi-agent network, where the goal of agents is to collectively minimize the sum of…

We study a fixed step-size noisy distributed gradient descent algorithm for solving optimization problems in which the objective is a finite sum of smooth but possibly non-convex functions. Random perturbations are introduced to the…

In this paper, we consider multi-stage stochastic optimization problems with convex objectives and conic constraints at each stage. We present a new stochastic first-order method, namely the dynamic stochastic approximation (DSA) algorithm,…

This paper proposes a fast decentralized algorithm for solving a consensus optimization problem defined in a directed networked multi-agent system, where the local objective functions have the smooth+nonsmooth composite form, and are…

Recently, many machine learning optimizers have been analysed considering them as the asymptotic limit of some differential equations when the step size goes to zero. In other words, the optimizers can be seen as a finite difference scheme…

In this report, we study decentralized stochastic optimization to minimize a sum of smooth and strongly convex cost functions when the functions are distributed over a directed network of nodes. In contrast to the existing work, we use…

Stochastic gradient descent is a canonical tool for addressing stochastic optimization problems, and forms the bedrock of modern machine learning and statistics. In this work, we seek to balance the fact that attenuating step-size is…

This note studies the distributed non-convex optimization problem with non-smooth regularization, which has wide applications in decentralized learning, estimation and control. The objective function is the sum of different local objective…

Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…

We develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm incorporates a variance reduction mechanism and the resulting…

This paper presents a novel distributed formulation of the min-max optimization problem. Such a formulation enables enhanced flexibility among agents when optimizing their maximization variables. To address the problem, we propose two…