Related papers: Low complexity convergence rate bounds for push-su…
We develop easily accessible quantities for bounding the almost sure exponential convergence rate of push-sum algorithms. We analyze the scenario of i.i.d. synchronous gossip, every agent communicating towards its single target at every…
The objective of the paper is to establish a computable upper bound for the almost sure convergence rate for a class of ratio consensus algorithms defined via column-stochastic matrices. Our result extends the works of Iutzeler et al.…
The problems discussed in this paper are motivated by general ratio consensus algorithms, introduced by Kempe, Dobra, and Gehrke (2003) in a simple form as the push-sum algorithm, later extended by B\'en\'ezit et al. (2010) under the name…
Finite-sum optimization plays an important role in the area of machine learning, and hence has triggered a surge of interest in recent years. To address this optimization problem, various randomized incremental gradient methods have been…
The push-sum based subgradient is an important method for distributed convex optimization over unbalanced directed graphs, which is known to converge at a rate of $O(\ln t/\sqrt{t})$. This paper shows that the subgradient-push algorithm…
We give almost sure convergence rate bounds of ratio consensus algorithms when the protocol can be reformulated to be linear updates of vector values on a possibly larger, augmented network. This is an improvement of the results of…
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…
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…
This article derives lower bounds on the convergence rate of continuous-time gradient-based optimization algorithms. The algorithms are subjected to a time-normalization constraint that avoids a reparametrization of time in order to make…
We develop a generic method for bounding the convergence rate of an averaging algorithm running in a multi-agent system with a time-varying network, where the associated stochastic matrices have a time-independent Perron vector. This method…
Quasi-convex optimization acts a pivotal part in many fields including economics and finance; the subgradient method is an effective iterative algorithm for solving large-scale quasi-convex optimization problems. In this paper, we…
We consider the precedence-constrained scheduling problem to minimize the total weighted completion time. For a single machine several $2$-approximation algorithms are known, which are based on linear programming and network flows. We show…
Classically, a control loop is designed to be executed strictly periodically. This is, however, difficult to achieve in many scenarios, for example, when overload or packet loss cannot be entirely avoided. Here, weakly-hard real-time…
Motivated by applications in machine learning and statistics, we study distributed optimization problems over a network of processors, where the goal is to optimize a global objective composed of a sum of local functions. In these problems,…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
In this paper, we study the problem of achieving average consensus over a random time-varying sequence of directed graphs by extending the class of so-called push-sum algorithms to such random scenarios. Provided that an ergodicity notion,…
We study the conditions under which one is able to efficiently apply variance-reduction and acceleration schemes on finite sum optimization problems. First, we show that, perhaps surprisingly, the finite sum structure by itself, is not…
The vast majority of convergence rates analysis for stochastic gradient methods in the literature focus on convergence in expectation, whereas trajectory-wise almost sure convergence is clearly important to ensure that any instantiation of…
We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the…
This article is devoted to propose some lower and upper bounds for the coupled-tasks scheduling problem in presence of compatibility constraints according to classical complexity hypothesis ($\mathcal{P} \neq \mathcal{NP}$,…