Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convexification of Learning from Constraints   Regularized empirical risk minimization with constrained labels (in contrast
to fixed labels) is a remarkably general abstraction of learning. For common
loss and regularization functions, this optimization problem assumes the form
of a mixed integer program (MIP) whose objective function is non-convex. In
this form, the problem is resistant to standard optimization techniques. We
construct MIPs with the same solutions whose objective functions are convex.
Specifically, we characterize the tightest convex extension of the objective
function, given by the Legendre-Fenchel biconjugate. Computing values of this
tightest convex extension is NP-hard. However, by applying our characterization
to every function in an additive decomposition of the objective function, we
obtain a class of looser convex extensions that can be computed efficiently.
For some decompositions, common loss and regularization functions, we derive a
closed form.

27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol