89 research outputs found
Efficient Sensitivity Analysis for Parametric Robust Markov Chains
We provide a novel method for sensitivity analysis of parametric robust Markov chains. These models incorporate parameters and sets of probability distributions to alleviate the often unrealistic assumption that precise probabilities are available. We measure sensitivity in terms of partial derivatives with respect to the uncertain transition probabilities regarding measures such as the expected reward. As our main contribution, we present an efficient method to compute these partial derivatives. To scale our approach to models with thousands of parameters, we present an extension of this method that selects the subset of parameters with the highest partial derivative. Our methods are based on linear programming and differentiating these programs around a given value for the parameters. The experiments show the applicability of our approach on models with over a million states and thousands of parameters. Moreover, we embed the results within an iterative learning scheme that profits from having access to a dedicated sensitivity analysis
Basic Polyhedral Theory
This is a chapter (planned to appear in Wiley's upcoming Encyclopedia of
Operations Research and Management Science) describing parts of the theory of
convex polyhedra that are particularly important for optimization. The topics
include polyhedral and finitely generated cones, the Weyl-Minkowski Theorem,
faces of polyhedra, projections of polyhedra, integral polyhedra, total dual
integrality, and total unimodularity.Comment: 14 page
Total unimodularity and the transportation problem: a generalization
AbstractWell-known sufficiency conditions for total unimodularity are relaxed to include more general classes of matrices, whose determinants are related to Fibonacci sequences. It is then shown that in order to study determinants of submatrices of the two-commodity transportation problem, one should study precisely these generalized unimodular matrices. (Note that all submatrices of an ordinary transportation problem are unimodular.) This result enables us to establish determinantal values for submatrices of two-commodity transportation problems (in terms of the number of disjoint capacitated routes) and to identify a totally unimodular class of two-commodity transportation problems
Efficient Sensitivity Analysis for Parametric Robust Markov Chains
We provide a novel method for sensitivity analysis of parametric robust
Markov chains. These models incorporate parameters and sets of probability
distributions to alleviate the often unrealistic assumption that precise
probabilities are available. We measure sensitivity in terms of partial
derivatives with respect to the uncertain transition probabilities regarding
measures such as the expected reward. As our main contribution, we present an
efficient method to compute these partial derivatives. To scale our approach to
models with thousands of parameters, we present an extension of this method
that selects the subset of parameters with the highest partial derivative.
Our methods are based on linear programming and differentiating these programs
around a given value for the parameters. The experiments show the applicability
of our approach on models with over a million states and thousands of
parameters. Moreover, we embed the results within an iterative learning scheme
that profits from having access to a dedicated sensitivity analysis.Comment: To be presented at CAV 202
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