Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robust Distributed Accelerated Stochastic Gradient Methods for
  Multi-Agent Networks   We study distributed stochastic gradient (D-SG) method and its accelerated
variant (D-ASG) for solving decentralized strongly convex stochastic
optimization problems where the objective function is distributed over several
computational units, lying on a fixed but arbitrary connected communication
graph, subject to local communication constraints where noisy estimates of the
gradients are available. We develop a framework which allows to choose the
stepsize and the momentum parameters of these algorithms in a way to optimize
performance by systematically trading off the bias, variance, robustness to
gradient noise and dependence to network effects. When gradients do not contain
noise, we also prove that distributed accelerated methods can \emph{achieve
acceleration}, requiring $\mathcal{O}(\kappa \log(1/\varepsilon))$ gradient
evaluations and $\mathcal{O}(\kappa \log(1/\varepsilon))$ communications to
converge to the same fixed point with the non-accelerated variant where
$\kappa$ is the condition number and $\varepsilon$ is the target accuracy. To
our knowledge, this is the first acceleration result where the iteration
complexity scales with the square root of the condition number in the context
of \emph{primal} distributed inexact first-order methods. For quadratic
functions, we also provide finer performance bounds that are tight with respect
to bias and variance terms. Finally, we study a multistage version of D-ASG
with parameters carefully varied over stages to ensure exact
$\mathcal{O}(-k/\sqrt{\kappa})$ linear decay in the bias term as well as
optimal $\mathcal{O}(\sigma^2/k)$ in the variance term. We illustrate through
numerical experiments that our approach results in practical algorithms that
are robust to gradient noise and that can outperform existing methods.

24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph