Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Online Frank-Wolfe with Unknown Delays   The online Frank-Wolfe (OFW) method has gained much popularity for online
convex optimization due to its projection-free property. Previous studies
showed that for convex losses, OFW attains $O(T^{3/4})$ regret over general
sets and $O(T^{2/3})$ regret over strongly convex sets, and if losses are
strongly convex, these bounds can be improved to $O(T^{2/3})$ and
$O(\sqrt{T})$, respectively. However, they assumed that each gradient queried
by OFW is revealed immediately, which may not hold in practice. In this paper,
we consider a more practical setting where gradients arrive with arbitrary and
unknown delays, and propose delayed OFW which generalizes OFW to this setting.
The main idea is to perform an update similar to OFW after receiving any
gradient, and play the latest decision for each round. We first show that for
convex losses, delayed OFW achieves $O(T^{3/4}+dT^{1/4})$ regret over general
sets and $O(T^{2/3}+dT^{1/3})$ regret over strongly convex sets, where $d$ is
the maximum delay. Furthermore, we prove that for strongly convex losses,
delayed OFW attains $O(T^{2/3}+d\log T)$ regret over general sets and
$O(\sqrt{T}+d\log T)$ regret over strongly convex sets. Compared with regret
bounds in the non-delayed setting, our results imply that the proposed method
is robust to a relatively large amount of delay.

19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat