Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Different Perspective On The Stochastic Convex Feasibility Problem   We analyze a simple randomized subgradient method for approximating solutions
to stochastic systems of convex functional constraints, the only input to the
algorithm being the size of minibatches. By introducing a new notion of what is
meant for a point to approximately solve the constraints, determining bounds on
the expected number of iterations reduces to determining a hitting time for a
compound Bernoulli process, elementary probability. Besides bounding the
expected number of iterations quite generally, we easily establish
concentration inequalities on the number of iterations, and more interesting,
we establish much-improved bounds when a notion akin to H\"{o}lderian growth is
satisfied, for all degrees of growth, not just the linear growth of
piecewise-linear convex functions or the quadratic growth of strongly convex
functions. Finally, we establish the analogous results under a slight
modification to the algorithm which results in the user knowing with high
confidence an iterate is in hand that approximately solves the system. Perhaps
surprisingly, the iteration bounds here are deterministic -- all of the
probability gets wrapped into the confidence level (albeit at the expense of
potentially large minibatches).

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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph