Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noisy Linear Convergence of Stochastic Gradient Descent for CV@R
  Statistical Learning under Polyak-{\L}ojasiewicz Conditions   Conditional Value-at-Risk ($\mathrm{CV@R}$) is one of the most popular
measures of risk, which has been recently considered as a performance criterion
in supervised statistical learning, as it is related to desirable operational
features in modern applications, such as safety, fairness, distributional
robustness, and prediction error stability. However, due to its variational
definition, $\mathrm{CV@R}$ is commonly believed to result in difficult
optimization problems, even for smooth and strongly convex loss functions. We
disprove this statement by establishing noisy (i.e., fixed-accuracy) linear
convergence of stochastic gradient descent for sequential $\mathrm{CV@R}$
learning, for a large class of not necessarily strongly-convex (or even convex)
loss functions satisfying a set-restricted Polyak-Lojasiewicz inequality. This
class contains all smooth and strongly convex losses, confirming that classical
problems, such as linear least squares regression, can be solved efficiently
under the $\mathrm{CV@R}$ criterion, just as their risk-neutral versions. Our
results are illustrated numerically on such a risk-aware ridge regression task,
also verifying their validity in practice.

30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc