Scenario Reduction Revisited: Fundamental Limits and Guarantees
Abstract
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 polynomialtime constantfactor approximations for both discrete and continuous scenario reduction as well as the first exact exponentialtime algorithms for continuous scenario reduction.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 arXiv:
 arXiv:1701.04072
 Bibcode:
 2017arXiv170104072R
 Keywords:

 Mathematics  Optimization and Control;
 Mathematics  Probability