Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Benefits of Multiple Gossip Steps in Communication-Constrained
  Decentralized Optimization   In decentralized optimization, it is common algorithmic practice to have
nodes interleave (local) gradient descent iterations with gossip (i.e.
averaging over the network) steps. Motivated by the training of large-scale
machine learning models, it is also increasingly common to require that
messages be {\em lossy compressed} versions of the local parameters. In this
paper, we show that, in such compressed decentralized optimization settings,
there are benefits to having {\em multiple} gossip steps between subsequent
gradient iterations, even when the cost of doing so is appropriately accounted
for e.g. by means of reducing the precision of compressed information. In
particular, we show that having $O(\log\frac{1}{\epsilon})$ gradient iterations
{with constant step size} - and $O(\log\frac{1}{\epsilon})$ gossip steps
between every pair of these iterations - enables convergence to within
$\epsilon$ of the optimal value for smooth non-convex objectives satisfying
Polyak-\L{}ojasiewicz condition. This result also holds for smooth strongly
convex objectives. To our knowledge, this is the first work that derives
convergence results for nonconvex optimization under arbitrary communication
compression.

12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph