1,979 research outputs found
Hamiltonian System Approach to Distributed Spectral Decomposition in Networks
Because of the significant increase in size and complexity of the networks,
the distributed computation of eigenvalues and eigenvectors of graph matrices
has become very challenging and yet it remains as important as before. In this
paper we develop efficient distributed algorithms to detect, with higher
resolution, closely situated eigenvalues and corresponding eigenvectors of
symmetric graph matrices. We model the system of graph spectral computation as
physical systems with Lagrangian and Hamiltonian dynamics. The spectrum of
Laplacian matrix, in particular, is framed as a classical spring-mass system
with Lagrangian dynamics. The spectrum of any general symmetric graph matrix
turns out to have a simple connection with quantum systems and it can be thus
formulated as a solution to a Schr\"odinger-type differential equation. Taking
into account the higher resolution requirement in the spectrum computation and
the related stability issues in the numerical solution of the underlying
differential equation, we propose the application of symplectic integrators to
the calculation of eigenspectrum. The effectiveness of the proposed techniques
is demonstrated with numerical simulations on real-world networks of different
sizes and complexities
Inverse Reinforcement Learning in Swarm Systems
Inverse reinforcement learning (IRL) has become a useful tool for learning
behavioral models from demonstration data. However, IRL remains mostly
unexplored for multi-agent systems. In this paper, we show how the principle of
IRL can be extended to homogeneous large-scale problems, inspired by the
collective swarming behavior of natural systems. In particular, we make the
following contributions to the field: 1) We introduce the swarMDP framework, a
sub-class of decentralized partially observable Markov decision processes
endowed with a swarm characterization. 2) Exploiting the inherent homogeneity
of this framework, we reduce the resulting multi-agent IRL problem to a
single-agent one by proving that the agent-specific value functions in this
model coincide. 3) To solve the corresponding control problem, we propose a
novel heterogeneous learning scheme that is particularly tailored to the swarm
setting. Results on two example systems demonstrate that our framework is able
to produce meaningful local reward models from which we can replicate the
observed global system dynamics.Comment: 9 pages, 8 figures; ### Version 2 ### version accepted at AAMAS 201
Methods to Improve Applicability and Efficiency of Distributed Data-Centric Compute Frameworks
The success of modern applications depends on the insights they collect from their data repositories. Data repositories for such applications currently exceed exabytes and are rapidly increasing in size, as they collect data from varied sources - web applications, mobile phones, sensors and other connected devices. Distributed storage and data-centric compute frameworks have been invented to store and analyze these large datasets. This dissertation focuses on extending the applicability and improving the efficiency of distributed data-centric compute frameworks
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