# Scenario reduction revisited: fundamental limits and guarantees

@article{Rujeerapaiboon2017ScenarioRR, title={Scenario reduction revisited: fundamental limits and guarantees}, author={Napat Rujeerapaiboon and Kilian Schindler and Daniel Kuhn and Wolfram Wiesemann}, journal={Mathematical Programming}, year={2017}, pages={1-36} }

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…

## 16 Citations

Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution

- Computer Science, MathematicsArXiv
- 2021

It is proved that computing the Wasserstein distance between a discrete probability measure supported on two points and the Lebesgue measure on the standard hypercube is already #P-hard, and it is shown that smoothing the dual objective function is equivalent to regularizing the primal objective function.

Problem-Driven Scenario Clustering in Stochastic Optimization

- Mathematics
- 2021

In stochastic optimisation, the large number of scenarios required to faithfully represent the underlying uncertainty is often a barrier to finding efficient numerical solutions. This motivates the…

Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning

- Computer Science, MathematicsOperations Research & Management Science in the Age of Analytics
- 2019

This tutorial argues that Wasserstein distributionally robust optimization has interesting ramifications for statistical learning and motivates new approaches for fundamental learning tasks such as classification, regression, maximum likelihood estimation or minimum mean square error estimation, among others.

An Information Theoretic Approach to Probability Mass Function Truncation

- Mathematics, Computer Science2019 IEEE International Symposium on Information Theory (ISIT)
- 2019

This paper proposes and analyzes a few criteria to truncate pmf’s so that the truncated one is as much close as possible to the original pmf, under different information theoretic measures of distance.

Scenario Reduction for Stochastic Day-Ahead Scheduling: A Mixed Autoencoder Based Time-Series Clustering Approach

- Computer ScienceIEEE Transactions on Smart Grid
- 2021

A mixed autoencoder based clustering approach to select a reduced scenario set from high-dimensional time series and shows that the model outperforms the state of the art, in terms of statistical metrics and through empirical analysis.

Upper and Lower Bounds for Large Scale Multistage Stochastic Optimization Problems: Application to Microgrid Management

- Computer Science, Mathematics
- 2019

The decomposition methods are much faster than the SDDP method in terms of computation time, thus allowing to tackle problem instances incorporating more than 60 state variables in a Dynamic Programming framework.

Decentralized Multistage Optimization of Large-Scale Microgrids under Stochasticity

- Mathematics
- 2021

Microgrids are recognized as a relevant tool to absorb decentralized renewable energies in the energy mix. However, the sequential handling of multiple stochastic productions and demands, and of…

Distributionally Robust Optimization: A Review

- Computer Science, MathematicsArXiv
- 2019

Main concepts and contributions to DRO are surveyed, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization are surveyed.

Optimization-based Scenario Reduction for Data-Driven Two-stage Stochastic Optimization

- 2020

Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title. However, use of a template does not certify that the paper has…

Scenario generation by selection from historical data

- Computer ScienceComput. Manag. Sci.
- 2021

The methods range from standard sampling and k -means, through iterative sampling-based selection methods, to a new moment-based optimization approach, and are compared on a simple portfolio-optimization model.

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