Related papers: Distributed Gradient Flow: Nonsmoothness, Nonconve…
The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…
We study finite-time performance of a recently proposed distributed dual subgradient (DDSG) method for convex constrained multi-agent optimization problems. The algorithm enjoys performance guarantees on the last primal iterate, as opposed…
This paper proposes a novel dynamical system called the Multiobjective Balanced Gradient Flow (MBGF), offering a dynamical perspective for normalized gradient methods in a class of multi-objective optimization problems. Under certain…
For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is…
There has been a growing effort in studying the distributed optimization problem over a network. The objective is to optimize a global function formed by a sum of local functions, using only local computation and communication. Literature…
Gradient descent (GD) and stochastic gradient descent (SGD) are the workhorses of large-scale machine learning. While classical theory focused on analyzing the performance of these methods in convex optimization problems, the most notable…
Various distributed gradient descent algorithms for multi-agent optimization have incorporated the Nesterov accelerated gradient method, where the use of momentum enhances convergence rates. These algorithms have found broad applications in…
We develop and analyze an asynchronous algorithm for distributed convex optimization when the objective writes a sum of smooth functions, local to each worker, and a non-smooth function. Unlike many existing methods, our distributed…
In this paper, we consider the problem of minimizing the sum of nonconvex and possibly nonsmooth functions over a connected multi-agent network, where the agents have partial knowledge about the global cost function and can only access the…
In this article, we focus on solving a class of distributed optimization problems involving $n$ agents with the local objective function at every agent $i$ given by the difference of two convex functions $f_i$ and $g_i$…
In recent years, different types of distributed and parallel learning schemes have received increasing attention for their strong advantages in handling large-scale data information. In the information era, to face the big data challenges…
In this paper, a distributed optimization problem with general differentiable convex objective functions is studied for single-integrator and double-integrator multi-agent systems. Two distributed adaptive optimization algorithm is…
Distributed optimization has a rich history. It has demonstrated its effectiveness in many machine learning applications, etc. In this paper we study a subclass of distributed optimization, namely decentralized optimization in a non-smooth…
This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We…
This paper presents a special type of distributed optimization problems, where the summation of agents' local cost functions (i.e., global cost function) is convex, but each individual can be non-convex. Unlike most distributed optimization…
In this paper, we give a sharp analysis for Stochastic Gradient Descent (SGD) and prove that SGD is able to efficiently escape from saddle points and find an $(\epsilon, O(\epsilon^{0.5}))$-approximate second-order stationary point in…
We consider decentralized gradient-free optimization of minimizing Lipschitz continuous functions that satisfy neither smoothness nor convexity assumption. We propose two novel gradient-free algorithms, the Decentralized Gradient-Free…
Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments.…
Wasserstein gradient flow (WGF) is a common method to perform optimization over the space of probability measures. While WGF is guaranteed to converge to a first-order stationary point, for nonconvex functionals the converged solution does…
Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…