Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Accelerating Incremental Gradient Optimization with Curvature
  Information   This paper studies an acceleration technique for incremental aggregated
gradient ({\sf IAG}) method through the use of \emph{curvature} information for
solving strongly convex finite sum optimization problems. These optimization
problems of interest arise in large-scale learning applications. Our technique
utilizes a curvature-aided gradient tracking step to produce accurate gradient
estimates incrementally using Hessian information. We propose and analyze two
methods utilizing the new technique, the curvature-aided IAG ({\sf CIAG})
method and the accelerated CIAG ({\sf A-CIAG}) method, which are analogous to
gradient method and Nesterov's accelerated gradient method, respectively.
Setting $\kappa$ to be the condition number of the objective function, we prove
the $R$ linear convergence rates of $1 - \frac{4c_0 \kappa}{(\kappa+1)^2}$ for
the {\sf CIAG} method, and $1 - \sqrt{\frac{c_1}{2\kappa}}$ for the {\sf
A-CIAG} method, where $c_0,c_1 \leq 1$ are constants inversely proportional to
the distance between the initial point and the optimal solution. When the
initial iterate is close to the optimal solution, the $R$ linear convergence
rates match with the gradient and accelerated gradient method, albeit {\sf
CIAG} and {\sf A-CIAG} operate in an incremental setting with strictly lower
computation complexity. Numerical experiments confirm our findings. The source
codes used for this paper can be found on
\url{http://github.com/hoitowai/ciag/}.

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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn