Related papers: Distributed Gradient Tracking Methods with Guarant…
Non-convex optimization problems are ubiquitous in machine learning, especially in Deep Learning. While such complex problems can often be successfully optimized in practice by using stochastic gradient descent (SGD), theoretical analysis…
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…
Recently introduced distributed zeroth-order optimization (ZOO) algorithms have shown their utility in distributed reinforcement learning (RL). Unfortunately, in the gradient estimation process, almost all of them require random samples…
Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…
Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…
Stochastic gradient methods (SGMs) are predominant approaches for solving stochastic optimization. On smooth nonconvex problems, a few acceleration techniques have been applied to improve the convergence rate of SGMs. However, little…
In noncooperative Nash games, equilibria are often inefficient. This is exemplified by the Prisoner's Dilemma and was first provably shown in the 1980s. Since then, understanding the quality of Nash equilibrium (NE) received considerable…
Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…
Decentralized stochastic optimization has recently benefited from gradient tracking methods \cite{DSGT_Pu,DSGT_Xin} providing efficient solutions for large-scale empirical risk minimization problems. In Part I \cite{GT_SAGA} of this work,…
The distributed setting for Saddle Problems (SPs) has recently emerged as a framework for various modern applications in machine learning and multiagent systems. Despite its relevance, the theoretical foundations of this setting have not…
An increasing number of machine learning problems, such as robust or adversarial variants of existing algorithms, require minimizing a loss function that is itself defined as a maximum. Carrying a loop of stochastic gradient ascent (SGA)…
The dual challenges of prohibitive communication overhead and the impracticality of gradient computation due to data privacy or black-box constraints in distributed systems motivate this work on communication-constrained gradient-free…
Large-scale non-convex sparsity-constrained problems have recently gained extensive attention. Most existing deterministic optimization methods (e.g., GraSP) are not suitable for large-scale and high-dimensional problems, and thus…
This paper proposes Asynchronous Triggered Gradient Tracking, i.e., a distributed optimization algorithm to solve consensus optimization over networks with asynchronous communication. As a building block, we devise the continuous-time…
We present and analyze a stochastic distributed method (S-NEAR-DGD) that can tolerate inexact computation and inaccurate information exchange to alleviate the problems of costly gradient evaluations and bandwidth-limited communication in…
We consider distributed optimization under communication constraints for training deep learning models. We propose a new algorithm, whose parameter updates rely on two forces: a regular gradient step, and a corrective direction dictated by…
Gradient descent with momentum has been widely applied in various signal processing and machine learning tasks, demonstrating a notable empirical advantage over standard gradient descent. However, momentum-based distributed Riemannian…
We consider distributed optimization on undirected connected graphs. We propose a novel distributed conditional gradient method with (O(1/\sqrt{k})) convergence. Compared with existing methods, each iteration of our method uses both…
This paper studies a distributed policy gradient in collaborative multi-agent reinforcement learning (MARL), where agents over a communication network aim to find the optimal policy to maximize the average of all agents' local returns. Due…
In this paper, we investigate a general class of stochastic gradient descent (SGD) algorithms, called Conditioned SGD, based on a preconditioning of the gradient direction. Using a discrete-time approach with martingale tools, we establish…