This paper considers the distributed bandit convex optimization problem with
time-varying constraints. In this problem, the global loss function is the
average of all the local convex loss functions, which are unknown beforehand.
Each agent iteratively makes its own decision subject to time-varying
inequality constraints which can be violated but are fulfilled in the long run.
For a uniformly jointly strongly connected time-varying directed graph, a
distributed bandit online primal-dual projection algorithm with one-point
sampling is proposed. We show that sublinear dynamic network regret and network
cumulative constraint violation are achieved if the path-length of the
benchmark also increases in a sublinear manner. In addition, an
$\mathcal{O}({T^{3/4 + g}})$ static network regret bound and an $\mathcal{O}(
{{T^{1 – {g}/2}}} )$ network cumulative constraint violation bound are
established, where $T$ is the total number of iterations and $g \in ( {0,1/4}
)$ is a trade-off parameter. Moreover, a reduced static network regret bound
$\mathcal{O}( {{T^{2/3 + 4g /3}}} )$ is established for strongly convex local
loss functions. Finally, a numerical example is presented to validate the
theoretical results.

Este artículo explora los viajes en el tiempo y sus implicaciones.

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