Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Faster Convex Lipschitz Regression via 2-block ADMM   The task of approximating an arbitrary convex function arises in several
learning problems such as convex regression, learning with a difference of
convex (DC) functions, and approximating Bregman divergences. In this paper, we
show how a broad class of convex function learning problems can be solved via a
2-block ADMM approach, where updates for each block can be computed in closed
form. For the task of convex Lipschitz regression, we establish that our
proposed algorithm converges with iteration complexity of $
O(n\sqrt{d}/\epsilon)$ for a dataset $ X \in \mathbb R^{n\times d}$ and
$\epsilon > 0$. Combined with per-iteration computation complexity, our method
converges with the rate $O(n^3 d^{1.5}/\epsilon+n^2 d^{2.5}/\epsilon+n
d^3/\epsilon)$. This new rate improves the state of the art rate of
$O(n^5d^2/\epsilon)$ available by interior point methods if $d = o( n^4)$.
Further we provide similar solvers for DC regression and Bregman divergence
learning. Unlike previous approaches, our method is amenable to the use of
GPUs. We demonstrate on regression and metric learning experiments that our
approach is up to 30 times faster than the existing method, and produces
results that are comparable to state-of-the-art.

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The categories of this paper are: physics
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: math
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The categories of this paper are: eess