Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributed Variable Sample-Size Gradient-response and Best-response
  Schemes for Stochastic Nash Equilibrium Problems over Graphs   This paper considers a stochastic Nash game in which each player minimizes an
expectation valued composite objective. We make the following contributions.
(I) Under suitable monotonicity assumptions on the concatenated gradient map,
we derive optimal rate statements and oracle complexity bounds for the proposed
variable sample-size proximal stochastic gradient-response (VS-PGR) scheme when
the sample-size increases at a geometric rate. If the sample-size increases at
a polynomial rate of degree $v > 0$, the mean-squared errordecays at a
corresponding polynomial rate while the iteration and oracle complexities to
obtain an $\epsilon$-NE are $\mathcal{O}(1/\epsilon^{1/v})$ and
$\mathcal{O}(1/\epsilon^{1+1/v})$, respectively. (II) We then overlay (VS-PGR)
with a consensus phase with a view towards developing distributed protocols for
aggregative stochastic Nash games. In the resulting scheme, when the
sample-size and the consensus steps grow at a geometric and linear rate,
computing an $\epsilon$-NE requires similar iteration and oracle complexities
to (VS-PGR) with a communication complexity of
$\mathcal{O}(\ln^2(1/\epsilon))$; (III) Under a suitable contractive property
associated with the proximal best-response (BR) map, we design a variable
sample-size proximal BR (VS-PBR) scheme, where each player solves a
sample-average BR problem. Akin to (I), we also give the rate statements,
oracle and iteration complexity bounds. (IV) Akin to (II), the distributed
variant achieves similar iteration and oracle complexities to the centralized
(VS-PBR) with a communication complexity of $\mathcal{O}(\ln^2(1/\epsilon))$
when the communication rounds per iteration increase at a linear rate. Finally,
we present some preliminary numerics to provide empirical support for the rate
and complexity statements.

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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cs