Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributed Optimization Based on Gradient-tracking Revisited: Enhancing
  Convergence Rate via Surrogation   We study distributed multiagent optimization over (directed, time-varying)
graphs. We consider the minimization of $F+G$ subject to convex constraints,
where $F$ is the smooth strongly convex sum of the agent's losses and $G$ is a
nonsmooth convex function. We build on the SONATA algorithm: the algorithm
employs the use of surrogate objective functions in the agents' subproblems
(going thus beyond linearization, such as proximal-gradient) coupled with a
perturbed (push-sum) consensus mechanism that aims to track locally the
gradient of $F$. SONATA achieves precision $\epsilon>0$ on the objective value
in $\mathcal{O}(\kappa_g \log(1/\epsilon))$ gradient computations at each node
and $\tilde{\mathcal{O}}\big(\kappa_g (1-\rho)^{-1/2} \log(1/\epsilon)\big)$
communication steps, where $\kappa_g$ is the condition number of $F$ and $\rho$
characterizes the connectivity of the network. This is the first linear rate
result for distributed composite optimization; it also improves on existing
(non-accelerated) schemes just minimizing $F$, whose rate depends on much
larger quantities than $\kappa_g$ (e.g., the worst-case condition number among
the agents). When considering in particular empirical risk minimization
problems with statistically similar data across the agents, SONATA employing
high-order surrogates achieves precision $\epsilon>0$ in
$\mathcal{O}\big((\beta/\mu) \log(1/\epsilon)\big)$ iterations and
$\tilde{\mathcal{O}}\big((\beta/\mu) (1-\rho)^{-1/2} \log(1/\epsilon)\big)$
communication steps, where $\beta$ measures the degree of similarity of the
agents' losses and $\mu$ is the strong convexity constant of $F$. Therefore,
when $\beta/\mu < \kappa_g$, the use of high-order surrogates yields provably
faster rates than what achievable by first-order models; this is without
exchanging any Hessian matrix over the network.

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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph