Related papers: Convergence Rate of Accelerated Average Consensus …
We extend the Approximate-Proximal Point (aProx) family of model-based methods for solving stochastic convex optimization problems, including stochastic subgradient, proximal point, and bundle methods, to the minibatch and accelerated…
Optimization plays a central role in intelligent systems and cyber-physical technologies, where speed and reliability of convergence directly impact performance. In control theory, optimization-centric methods are standard: controllers are…
A standard way to obtain convergence guarantees in stochastic convex optimization is to run an online learning algorithm and then output the average of its iterates: the actual iterates of the online learning algorithm do not come with…
We present a novel way of generating Lyapunov functions for proving linear convergence rates of first-order optimization methods. Our approach provably obtains the fastest linear convergence rate that can be verified by a quadratic Lyapunov…
We extend a multi-agent convex-optimization algorithm named Newton-Raphson consensus to a network scenario that involves directed, asynchronous and lossy communications. We theoretically analyze the stability and performance of the…
Recent studies have illustrated that stochastic gradient Markov Chain Monte Carlo techniques have a strong potential in non-convex optimization, where local and global convergence guarantees can be shown under certain conditions. By…
The present paper is devoted to estimating the speed of convergence towards consensus for a general class of discrete-time multi-agent systems. In the systems considered here, both the topology of the interconnection graph and the weight of…
This paper presents a novel accelerated distributed algorithm for unconstrained consensus optimization over static undirected networks. The proposed algorithm combines the benefits of acceleration from momentum, the robustness of the…
Partially observable Markov decision processes (POMDPs) have recently become popular among many AI researchers because they serve as a natural model for planning under uncertainty. Value iteration is a well-known algorithm for finding…
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,…
Alternating Direction Method of Multipliers (ADMM) is a popular convex optimization algorithm, which can be employed for solving distributed consensus optimization problems. In this setting agents locally estimate the optimal solution of an…
Maximum a posteriori (MAP) inference is a fundamental computational paradigm for statistical inference. In the setting of graphical models, MAP inference entails solving a combinatorial optimization problem to find the most likely…
We study the performance of asymptotic and approximate consensus algorithms under harsh environmental conditions. The asymptotic consensus problem requires a set of agents to repeatedly set their outputs such that the outputs converge to a…
Despite the broad use of fixed-point iterations throughout applied mathematics, the optimal convergence rate of general fixed-point problems with nonexpansive nonlinear operators has not been established. This work presents an acceleration…
We consider the matching augmentation problem (MAP), where a matching of a graph needs to be extended into a $2$-edge-connected spanning subgraph by adding the minimum number of edges to it. We present a polynomial-time algorithm with an…
In the rapidly evolving research on artificial intelligence (AI) the demand for fast, computationally efficient, and scalable solutions has increased in recent years. The problem of optimizing the computing resources for distributed machine…
This paper considers time-average stochastic optimization, where a time average decision vector, an average of decision vectors chosen in every time step from a time-varying (possibly non-convex) set, minimizes a convex objective function…
Several new accelerated methods in minimax optimization and fixed-point iterations have recently been discovered, and, interestingly, they rely on a mechanism distinct from Nesterov's momentum-based acceleration. In this work, we show that…
Efficient data access in High-Performance Computing (HPC) systems is essential to the performance of intensive computing tasks. Traditional optimizations of the I/O stack aim to improve peak performance but are often workload specific and…
In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…