Scenario reduction revisited: fundamental limits and guarantees

The goal of scenario reduction is to approximate a given discrete distribution with another discrete distribution that has fewer atoms. We distinguish continuous scenario reduction, where the new atoms may be chosen freely, and discrete scenario reduction, where the new atoms must be chosen from amo...

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Bibliographic Details
Published in:Mathematical programming Vol. 191; no. 1; pp. 207 - 242
Main Authors: Rujeerapaiboon, Napat, Schindler, Kilian, Kuhn, Daniel, Wiesemann, Wolfram
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2022
Springer
Springer Nature B.V
Subjects:
Algorithms
Approximation
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Cost control
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Polynomials
Probability
Probability distribution
Reduction
Theoretical
Time constant
Wasserstein distance
means clustering
Scenario reduction
median clustering
Constant-factor approximation algorithm
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary:The goal of scenario reduction is to approximate a given discrete distribution with another discrete distribution that has fewer atoms. We distinguish continuous scenario reduction, where the new atoms may be chosen freely, and discrete scenario reduction, where the new atoms must be chosen from among the existing ones. Using the Wasserstein distance as measure of proximity between distributions, we identify those n -point distributions on the unit ball that are least susceptible to scenario reduction, i.e., that have maximum Wasserstein distance to their closest m -point distributions for some prescribed m < n . We also provide sharp bounds on the added benefit of continuous over discrete scenario reduction. Finally, to our best knowledge, we propose the first polynomial-time constant-factor approximations for both discrete and continuous scenario reduction as well as the first exact exponential-time algorithms for continuous scenario reduction.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-018-1269-1