相关论文: Subgradient-Push Is of the Optimal Convergence Rat…

The push-sum algorithm is probably the most important distributed averaging approach over directed graphs, which has been applied to various problems including distributed optimization. This paper establishes the explicit absolute…

We investigate the convergence rate of the recently proposed subgradient-push method for distributed optimization over time-varying directed graphs. The subgradient-push method can be implemented in a distributed way without requiring…

The paper proposes a heterogeneous push-sum based subgradient algorithm for multi-agent distributed convex optimization in which each agent can arbitrarily switch between subgradient-push and push-subgradient at each time. It is shown that…

We consider distributed optimization by a collection of nodes, each having access to its own convex function, whose collective goal is to minimize the sum of the functions. The communications between nodes are described by a time-varying…

We consider the distributed optimization problem for the sum of convex functions where the underlying communications network connecting agents at each time is drawn at random from a collection of directed graphs. Building on an earlier work…

Distributed optimization has recieved a lot of interest due to its wide applications in various fields. It consists of multiple agents that connected by a graph and optimize a total cost in a collaborative way. Often in the applications,…

We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. We generalize the results…

The gradient-push algorithm is a fundamental algorithm for the distributed optimization problem \begin{equation} \min_{x \in \mathbb{R}^d} f(x) = \sum_{j=1}^n f_j (x), \end{equation} where each local cost $f_j$ is only known to agent $a_i$…

In this paper, we focus on solving a distributed convex optimization problem in a network, where each agent has its own convex cost function and the goal is to minimize the sum of the agents' cost functions while obeying the network…

We consider a multi agent optimization problem where a set of agents collectively solves a global optimization problem with the objective function given by the sum of locally known convex functions. We focus on the case when information…

In this paper, we focus on solving a distributed convex optimization problem in a network, where each agent has its own convex cost function and the goal is to minimize the sum of the agents' cost functions while obeying the network…

In this letter, we study distributed optimization, where a network of agents, abstracted as a directed graph, collaborates to minimize the average of locally-known convex functions. Most of the existing approaches over directed graphs are…

A lot of effort has been invested into characterizing the convergence rates of gradient based algorithms for non-linear convex optimization. Recently, motivated by large datasets and problems in machine learning, the interest has shifted…

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 extend the classic convergence rate theory for subgradient methods to apply to non-Lipschitz functions. For the deterministic projected subgradient method, we present a global $O(1/\sqrt{T})$ convergence rate for any convex function…

This paper considers convex programs with a general (possibly non-differentiable) convex objective function and Lipschitz continuous convex inequality constraint functions. A simple algorithm is developed and achieves an $O(1/t)$…

It is well known that the optimal convergence rate for stochastic optimization of smooth functions is $O(1/\sqrt{T})$, which is same as stochastic optimization of Lipschitz continuous convex functions. This is in contrast to optimizing…

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…

Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…

In this note, we present a new averaging technique for the projected stochastic subgradient method. By using a weighted average with a weight of t+1 for each iterate w_t at iteration t, we obtain the convergence rate of O(1/t) with both an…