Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Big-Step-Little-Step: Efficient Gradient Methods for Objectives with
  Multiple Scales   We provide new gradient-based methods for efficiently solving a broad class
of ill-conditioned optimization problems. We consider the problem of minimizing
a function $f : \mathbb{R}^d \rightarrow \mathbb{R}$ which is implicitly
decomposable as the sum of $m$ unknown non-interacting smooth, strongly convex
functions and provide a method which solves this problem with a number of
gradient evaluations that scales (up to logarithmic factors) as the product of
the square-root of the condition numbers of the components. This complexity
bound (which we prove is nearly optimal) can improve almost exponentially on
that of accelerated gradient methods, which grow as the square root of the
condition number of $f$. Additionally, we provide efficient methods for solving
stochastic, quadratic variants of this multiscale optimization problem. Rather
than learn the decomposition of $f$ (which would be prohibitively expensive),
our methods apply a clean recursive "Big-Step-Little-Step" interleaving of
standard methods. The resulting algorithms use $\tilde{\mathcal{O}}(d m)$
space, are numerically stable, and open the door to a more fine-grained
understanding of the complexity of convex optimization beyond condition number.

33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin