Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A General Analysis Framework of Lower Complexity Bounds for Finite-Sum
  Optimization   This paper studies the lower bound complexity for the optimization problem
whose objective function is the average of $n$ individual smooth convex
functions. We consider the algorithm which gets access to gradient and proximal
oracle for each individual component. For the strongly-convex case, we prove
such an algorithm can not reach an $\varepsilon$-suboptimal point in fewer than
$\Omega((n+\sqrt{\kappa n})\log(1/\varepsilon))$ iterations, where $\kappa$ is
the condition number of the objective function. This lower bound is tighter
than previous results and perfectly matches the upper bound of the existing
proximal incremental first-order oracle algorithm Point-SAGA. We develop a
novel construction to show the above result, which partitions the tridiagonal
matrix of classical examples into $n$ groups. This construction is friendly to
the analysis of proximal oracle and also could be used to general convex and
average smooth cases naturally.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
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The categories of this paper are: physics
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
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The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph