Submodular Functions: Learnability, Structure, and Optimization
نویسندگان
چکیده
منابع مشابه
Submodular Functions: Learnability, Structure, and Optimization
Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In this work we study submodular functions from a learning theoretic angle. We provide algorithms for learning submodular functions, as well as lower bounds on the...
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Submodular functions are discrete analogue of convex functions, arising in various fields of applied mathematics including game theory, information theory, and queueing theory. This survey aims at providing an overview on fundamental properties of submodular functions and recent algorithmic developments of their optimization and approximation. For submodular function minimization, the ellipsoid...
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In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it is beneficial to have strong guarantees on the tractable approximate solutions. In order operate under these criterion most optimization problems are cast und...
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Submodular functions are the discrete ananlogue of convexity and generalize many known and well studied settings. They capture several economic principles such as decreasing marginal cost and correlated utilities. Multi-agent allocation problems over submodular functions arise in a variety of natural scenarios and have been the subject of extensive study over the last decade. In this proposal I...
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Set-functions appear in many areas of computer science and applied mathematics, such as machine learning [1, 2, 3, 4], computer vision [5, 6], operations research [7] or electrical networks [8]. Among these set-functions, submodular functions play an important role, similar to convex functions on vector spaces. In this tutorial, the theory of submodular functions is presented, in a self-contain...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2018
ISSN: 0097-5397,1095-7111
DOI: 10.1137/120888909