Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thinking Outside the Ball: Optimal Learning with Gradient Descent for
  Generalized Linear Stochastic Convex Optimization   We consider linear prediction with a convex Lipschitz loss, or more
generally, stochastic convex optimization problems of generalized linear form,
i.e.~where each instantaneous loss is a scalar convex function of a linear
function. We show that in this setting, early stopped Gradient Descent (GD),
without any explicit regularization or projection, ensures excess error at most
$\epsilon$ (compared to the best possible with unit Euclidean norm) with an
optimal, up to logarithmic factors, sample complexity of
$\tilde{O}(1/\epsilon^2)$ and only $\tilde{O}(1/\epsilon^2)$ iterations. This
contrasts with general stochastic convex optimization, where
$\Omega(1/\epsilon^4)$ iterations are needed Amir et al. [2021b]. The lower
iteration complexity is ensured by leveraging uniform convergence rather than
stability. But instead of uniform convergence in a norm ball, which we show can
guarantee suboptimal learning using $\Theta(1/\epsilon^4)$ samples, we rely on
uniform convergence in a distribution-dependent ball.

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The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg