10,493 research outputs found
Accelerated Backpressure Algorithm
We develop an Accelerated Back Pressure (ABP) algorithm using Accelerated
Dual Descent (ADD), a distributed approximate Newton-like algorithm that only
uses local information. Our construction is based on writing the backpressure
algorithm as the solution to a network feasibility problem solved via
stochastic dual subgradient descent. We apply stochastic ADD in place of the
stochastic gradient descent algorithm. We prove that the ABP algorithm
guarantees stable queues. Our numerical experiments demonstrate a significant
improvement in convergence rate, especially when the packet arrival statistics
vary over time.Comment: 9 pages, 4 figures. A version of this work with significantly
extended proofs is being submitted for journal publicatio
Multi-consensus Decentralized Accelerated Gradient Descent
This paper considers the decentralized optimization problem, which has
applications in large scale machine learning, sensor networks, and control
theory. We propose a novel algorithm that can achieve near optimal
communication complexity, matching the known lower bound up to a logarithmic
factor of the condition number of the problem. Our theoretical results give
affirmative answers to the open problem on whether there exists an algorithm
that can achieve a communication complexity (nearly) matching the lower bound
depending on the global condition number instead of the local one. Moreover,
the proposed algorithm achieves the optimal computation complexity matching the
lower bound up to universal constants. Furthermore, to achieve a linear
convergence rate, our algorithm \emph{doesn't} require the individual functions
to be (strongly) convex. Our method relies on a novel combination of known
techniques including Nesterov's accelerated gradient descent, multi-consensus
and gradient-tracking. The analysis is new, and may be applied to other related
problems. Empirical studies demonstrate the effectiveness of our method for
machine learning applications
An Accelerated Decentralized Stochastic Proximal Algorithm for Finite Sums
Modern large-scale finite-sum optimization relies on two key aspects:
distribution and stochastic updates. For smooth and strongly convex problems,
existing decentralized algorithms are slower than modern accelerated
variance-reduced stochastic algorithms when run on a single machine, and are
therefore not efficient. Centralized algorithms are fast, but their scaling is
limited by global aggregation steps that result in communication bottlenecks.
In this work, we propose an efficient \textbf{A}ccelerated
\textbf{D}ecentralized stochastic algorithm for \textbf{F}inite \textbf{S}ums
named ADFS, which uses local stochastic proximal updates and randomized
pairwise communications between nodes. On machines, ADFS learns from
samples in the same time it takes optimal algorithms to learn from samples
on one machine. This scaling holds until a critical network size is reached,
which depends on communication delays, on the number of samples , and on the
network topology. We provide a theoretical analysis based on a novel augmented
graph approach combined with a precise evaluation of synchronization times and
an extension of the accelerated proximal coordinate gradient algorithm to
arbitrary sampling. We illustrate the improvement of ADFS over state-of-the-art
decentralized approaches with experiments.Comment: Code available in source files. arXiv admin note: substantial text
overlap with arXiv:1901.0986
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