Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence and Stability of the Stochastic Proximal Point Algorithm
  with Momentum   Stochastic gradient descent with momentum (SGDM) is the dominant algorithm in
many optimization scenarios, including convex optimization instances and
non-convex neural network training. Yet, in the stochastic setting, momentum
interferes with gradient noise, often leading to specific step size and
momentum choices in order to guarantee convergence, set aside acceleration.
Proximal point methods, on the other hand, have gained much attention due to
their numerical stability and elasticity against imperfect tuning. Their
stochastic accelerated variants though have received limited attention: how
momentum interacts with the stability of (stochastic) proximal point methods
remains largely unstudied. To address this, we focus on the convergence and
stability of the stochastic proximal point algorithm with momentum (SPPAM), and
show that SPPAM allows a faster linear convergence to a neighborhood compared
to stochastic proximal point algorithm (SPPA) with a better contraction factor,
under proper hyperparameter tuning. In terms of stability, we show that SPPAM
depends on problem constants more favorably than SGDM, allowing a wider range
of step size and momentum that lead to convergence.

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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci