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    Distributed Submodular Minimization And Motion Coordination Over Discrete State Space

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    1709.07379v2.pdf
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    Type
    Preprint
    Authors
    Jaleel, Hassan
    Shamma, Jeff S. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering Program
    Date
    2017-09-21
    Permanent link to this record
    http://hdl.handle.net/10754/626487
    
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    Abstract
    Submodular set-functions are extensively used in large-scale combinatorial optimization problems arising in complex networks and machine learning. While there has been significant interest in distributed formulations of convex optimization, distributed minimization of submodular functions has not received significant attention. Thus, our main contribution is a framework for minimizing submodular functions in a distributed manner. The proposed framework is based on the ideas of Lovasz extension of submodular functions and distributed optimization of convex functions. The framework exploits a fundamental property of submodularity that the Lovasz extension of a submodular function is a convex function and can be computed efficiently. Moreover, a minimizer of a submodular function can be computed by computing the minimizer of its Lovasz extension. In the proposed framework, we employ a consensus based distributed optimization algorithm to minimize set-valued submodular functions as well as general submodular functions defined over set products. We also identify distributed motion coordination in multiagent systems as a new application domain for submodular function minimization. For demonstrating key ideas of the proposed framework, we select a complex setup of the capture the flag game, which offers a variety of challenges relevant to multiagent system. We formulate the problem as a submodular minimization problem and verify through extensive simulations that the proposed framework results in feasible policies for the agents.
    Publisher
    arXiv
    arXiv
    1709.07379
    Additional Links
    http://arxiv.org/abs/1709.07379v2
    http://arxiv.org/pdf/1709.07379v2
    Collections
    Preprints; Electrical and Computer Engineering Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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