ROADEF 2020, Plénière, vendredi 21 février 2020, Wolfram Wiesemann (Imperial College Business School, London, U.K.) [March 11, 2020]

 Summary

Data-Driven Chance Constrained Programs

Chance constrained programs, which seek for a cost-optimal decision that satisfies a set of uncertain constraints with a pre-specified probability, constitute a popular and versatile method for decision-making under uncertainty. Since the true distribution governing the uncertain problem parameters is typically not known and thus has to be estimated from data, chance constrained programs often suffer from overfitting. In this talk, we study data-driven chance constrained programs that combat the issue of overfitting by  hedging against all distributions sufficiently close to the empirical one, where proximity is measured by the Wasserstein distance. For individual chance constraints as well as joint chance constraints with right-hand side uncertainty, we provide exact mixed-integer conic programming reformulations. Using our reformulation, we show that two popular approximation schemes based on the conditional-value-at-risk and the Bonferroni inequality can perform poorly in practice. We conclude with numerical results.

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