29,463 research outputs found
Persistent Monitoring of Events with Stochastic Arrivals at Multiple Stations
This paper introduces a new mobile sensor scheduling problem, involving a
single robot tasked with monitoring several events of interest that occur at
different locations. Of particular interest is the monitoring of transient
events that can not be easily forecast. Application areas range from natural
phenomena ({\em e.g.}, monitoring abnormal seismic activity around a volcano
using a ground robot) to urban activities ({\em e.g.}, monitoring early
formations of traffic congestion using an aerial robot). Motivated by those and
many other examples, this paper focuses on problems in which the precise
occurrence times of the events are unknown {\em a priori}, but statistics for
their inter-arrival times are available. The robot's task is to monitor the
events to optimize the following two objectives: {\em (i)} maximize the number
of events observed and {\em (ii)} minimize the delay between two consecutive
observations of events occurring at the same location. The paper considers the
case when a robot is tasked with optimizing the event observations in a
balanced manner, following a cyclic patrolling route. First, assuming the
cyclic ordering of stations is known, we prove the existence and uniqueness of
the optimal solution, and show that the optimal solution has desirable
convergence and robustness properties. Our constructive proof also produces an
efficient algorithm for computing the unique optimal solution with time
complexity, in which is the number of stations, with time
complexity for incrementally adding or removing stations. Except for the
algorithm, most of the analysis remains valid when the cyclic order is unknown.
We then provide a polynomial-time approximation scheme that gives a
-optimal solution for this more general, NP-hard problem
Exponentially Fast Parameter Estimation in Networks Using Distributed Dual Averaging
In this paper we present an optimization-based view of distributed parameter
estimation and observational social learning in networks. Agents receive a
sequence of random, independent and identically distributed (i.i.d.) signals,
each of which individually may not be informative about the underlying true
state, but the signals together are globally informative enough to make the
true state identifiable. Using an optimization-based characterization of
Bayesian learning as proximal stochastic gradient descent (with
Kullback-Leibler divergence from a prior as a proximal function), we show how
to efficiently use a distributed, online variant of Nesterov's dual averaging
method to solve the estimation with purely local information. When the true
state is globally identifiable, and the network is connected, we prove that
agents eventually learn the true parameter using a randomized gossip scheme. We
demonstrate that with high probability the convergence is exponentially fast
with a rate dependent on the KL divergence of observations under the true state
from observations under the second likeliest state. Furthermore, our work also
highlights the possibility of learning under continuous adaptation of network
which is a consequence of employing constant, unit stepsize for the algorithm.Comment: 6 pages, To appear in Conference on Decision and Control 201
A spatial mixed Poisson framework for combination of excess-of-loss and proportional reinsurance contracts
In this paper a purely theoretical reinsurance model is presented, where the reinsurance contract is assumed to be simultaneously of an excess-of-loss and of a proportional type. The stochastic structure of the set of pairs (claim’s arrival time, claim’s size) is described by a Spatial Mixed Poisson Process. By using an invariance property of the Spatial Mixed Poisson Processes, we estimate the amount that the ceding company obtains in a fixed time interval in force of the reinsurance contract
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