Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gradient Free Minimax Optimization: Variance Reduction and Faster
  Convergence   Many important machine learning applications amount to solving minimax
optimization problems, and in many cases there is no access to the gradient
information, but only the function values. In this paper, we focus on such a
gradient-free setting, and consider the nonconvex-strongly-concave minimax
stochastic optimization problem. In the literature, various zeroth-order (i.e.,
gradient-free) minimax methods have been proposed, but none of them achieve the
potentially feasible computational complexity of $\mathcal{O}(\epsilon^{-3})$
suggested by the stochastic nonconvex minimization theorem. In this paper, we
adopt the variance reduction technique to design a novel zeroth-order variance
reduced gradient descent ascent (ZO-VRGDA) algorithm. We show that the ZO-VRGDA
algorithm achieves the best known query complexity of $\mathcal{O}(\kappa(d_1 +
d_2)\epsilon^{-3})$, which outperforms all previous complexity bound by orders
of magnitude, where $d_1$ and $d_2$ denote the dimensions of the optimization
variables and $\kappa$ denotes the condition number. In particular, with a new
analysis technique that we develop, our result does not rely on a diminishing
or accuracy-dependent stepsize usually required in the existing methods. To our
best knowledge, this is the first study of zeroth-order minimax optimization
with variance reduction. Experimental results on the black-box distributional
robust optimization problem demonstrates the advantageous performance of our
new algorithm.

31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph