Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity Lower Bounds for Nonconvex-Strongly-Concave Min-Max
  Optimization   We provide a first-order oracle complexity lower bound for finding stationary
points of min-max optimization problems where the objective function is smooth,
nonconvex in the minimization variable, and strongly concave in the
maximization variable. We establish a lower bound of
$\Omega\left(\sqrt{\kappa}\epsilon^{-2}\right)$ for deterministic oracles,
where $\epsilon$ defines the level of approximate stationarity and $\kappa$ is
the condition number. Our analysis shows that the upper bound achieved in (Lin
et al., 2020b) is optimal in the $\epsilon$ and $\kappa$ dependence up to
logarithmic factors. For stochastic oracles, we provide a lower bound of
$\Omega\left(\sqrt{\kappa}\epsilon^{-2} + \kappa^{1/3}\epsilon^{-4}\right)$. It
suggests that there is a significant gap between the upper bound
$\mathcal{O}(\kappa^3 \epsilon^{-4})$ in (Lin et al., 2020a) and our lower
bound in the condition number dependence.

15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin