70,951 research outputs found
Pursuit on a Graph Using Partial Information
The optimal control of a "blind" pursuer searching for an evader moving on a
road network and heading at a known speed toward a set of goal vertices is
considered. To aid the "blind" pursuer, certain roads in the network have been
instrumented with Unattended Ground Sensors (UGSs) that detect the evader's
passage. When the pursuer arrives at an instrumented node, the UGS therein
informs the pursuer if and when the evader visited the node. The pursuer's
motion is not restricted to the road network. In addition, the pursuer can
choose to wait/loiter for an arbitrary time at any UGS location/node. At time
0, the evader passes by an entry node on his way towards one of the exit nodes.
The pursuer also arrives at this entry node after some delay and is thus
informed about the presence of the intruder/evader in the network, whereupon
the chase is on - the pursuer is tasked with capturing the evader. Because the
pursuer is "blind", capture entails the pursuer and evader being collocated at
an UGS location. If this happens, the UGS is triggered and this information is
instantaneously relayed to the pursuer, thereby enabling capture. On the other
hand, if the evader reaches one of the exit nodes without being captured, he is
deemed to have escaped. We provide an algorithm that computes the maximum
initial delay at the entry node for which capture is guaranteed. The algorithm
also returns the corresponding optimal pursuit policy
Dynamic Compressive Sensing of Time-Varying Signals via Approximate Message Passing
In this work the dynamic compressive sensing (CS) problem of recovering
sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear
measurements is explored from a Bayesian perspective. While there has been a
handful of previously proposed Bayesian dynamic CS algorithms in the
literature, the ability to perform inference on high-dimensional problems in a
computationally efficient manner remains elusive. In response, we propose a
probabilistic dynamic CS signal model that captures both amplitude and support
correlation structure, and describe an approximate message passing algorithm
that performs soft signal estimation and support detection with a computational
complexity that is linear in all problem dimensions. The algorithm, DCS-AMP,
can perform either causal filtering or non-causal smoothing, and is capable of
learning model parameters adaptively from the data through an
expectation-maximization learning procedure. We provide numerical evidence that
DCS-AMP performs within 3 dB of oracle bounds on synthetic data under a variety
of operating conditions. We further describe the result of applying DCS-AMP to
two real dynamic CS datasets, as well as a frequency estimation task, to
bolster our claim that DCS-AMP is capable of offering state-of-the-art
performance and speed on real-world high-dimensional problems.Comment: 32 pages, 7 figure
Deep Reinforcement Learning for Swarm Systems
Recently, deep reinforcement learning (RL) methods have been applied
successfully to multi-agent scenarios. Typically, these methods rely on a
concatenation of agent states to represent the information content required for
decentralized decision making. However, concatenation scales poorly to swarm
systems with a large number of homogeneous agents as it does not exploit the
fundamental properties inherent to these systems: (i) the agents in the swarm
are interchangeable and (ii) the exact number of agents in the swarm is
irrelevant. Therefore, we propose a new state representation for deep
multi-agent RL based on mean embeddings of distributions. We treat the agents
as samples of a distribution and use the empirical mean embedding as input for
a decentralized policy. We define different feature spaces of the mean
embedding using histograms, radial basis functions and a neural network learned
end-to-end. We evaluate the representation on two well known problems from the
swarm literature (rendezvous and pursuit evasion), in a globally and locally
observable setup. For the local setup we furthermore introduce simple
communication protocols. Of all approaches, the mean embedding representation
using neural network features enables the richest information exchange between
neighboring agents facilitating the development of more complex collective
strategies.Comment: 31 pages, 12 figures, version 3 (published in JMLR Volume 20
Compressive Network Analysis
Modern data acquisition routinely produces massive amounts of network data.
Though many methods and models have been proposed to analyze such data, the
research of network data is largely disconnected with the classical theory of
statistical learning and signal processing. In this paper, we present a new
framework for modeling network data, which connects two seemingly different
areas: network data analysis and compressed sensing. From a nonparametric
perspective, we model an observed network using a large dictionary. In
particular, we consider the network clique detection problem and show
connections between our formulation with a new algebraic tool, namely Randon
basis pursuit in homogeneous spaces. Such a connection allows us to identify
rigorous recovery conditions for clique detection problems. Though this paper
is mainly conceptual, we also develop practical approximation algorithms for
solving empirical problems and demonstrate their usefulness on real-world
datasets
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