Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regret and Cumulative Constraint Violation Analysis for Distributed
  Online Constrained Convex Optimization   This paper considers the distributed online convex optimization problem with
time-varying constraints over a network of agents. This is a sequential
decision making problem with two sequences of arbitrarily varying convex loss
and constraint functions. At each round, each agent selects a decision from the
decision set, and then only a portion of the loss function and a coordinate
block of the constraint function at this round are privately revealed to this
agent. The goal of the network is to minimize the network-wide loss accumulated
over time. Two distributed online algorithms with full-information and bandit
feedback are proposed. Both dynamic and static network regret bounds are
analyzed for the proposed algorithms, and network cumulative constraint
violation is used to measure constraint violation, which excludes the situation
that strictly feasible constraints can compensate the effects of violated
constraints. In particular, we show that the proposed algorithms achieve
$\mathcal{O}(T^{\max\{\kappa,1-\kappa\}})$ static network regret and
$\mathcal{O}(T^{1-\kappa/2})$ network cumulative constraint violation, where
$T$ is the time horizon and $\kappa\in(0,1)$ is a user-defined trade-off
parameter. Moreover, if the loss functions are strongly convex, then the static
network regret bound can be reduced to $\mathcal{O}(T^{\kappa})$. Finally,
numerical simulations are provided to illustrate the effectiveness of the
theoretical results.

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The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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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: hep-th
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The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg