Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: ANITA: An Optimal Loopless Accelerated Variance-Reduced Gradient Method   In this paper, we propose a novel accelerated gradient method called ANITA
for solving the fundamental finite-sum optimization problems. Concretely, we
consider both general convex and strongly convex settings: i) For general
convex finite-sum problems, ANITA improves previous state-of-the-art result
given by Varag (Lan et al., 2019). In particular, for large-scale problems or
the target error is not very small, i.e., $n \geq \frac{1}{\epsilon^2}$, ANITA
obtains the \emph{first} optimal result $O(n)$, matching the lower bound
$\Omega(n)$ provided by Woodworth and Srebro (2016), while previous results are
$O(n \log \frac{1}{\epsilon})$ of Varag (Lan et al., 2019) and
$O(\frac{n}{\sqrt{\epsilon}})$ of Katyusha (Allen-Zhu, 2017). ii) For strongly
convex finite-sum problems, we also show that ANITA can achieve the optimal
convergence rate $O\big((n+\sqrt{\frac{nL}{\mu}})\log\frac{1}{\epsilon}\big)$
matching the lower bound
$\Omega\big((n+\sqrt{\frac{nL}{\mu}})\log\frac{1}{\epsilon}\big)$ provided by
Lan and Zhou (2015). Besides, ANITA enjoys a simpler loopless algorithmic
structure unlike previous accelerated algorithms such as Varag (Lan et al.,
2019) and Katyusha (Allen-Zhu, 2017) where they use an inconvenient double-loop
structure. Moreover, by exploiting the loopless structure of ANITA, we provide
a new \emph{dynamic multi-stage convergence analysis}, which is the key
technical part for improving previous results to the optimal rates. Finally,
the numerical experiments show that ANITA converges faster than the previous
state-of-the-art Varag (Lan et al., 2019), validating our theoretical results
and confirming the practical superiority of ANITA. We believe that our new
theoretical rates and convergence analysis for this fundamental finite-sum
problem will directly lead to key improvements for many other related problems,
such as distributed/federated/decentralized optimization problems.

15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th