Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness, optimizing over a chance constrained set is challenging. In this project, we aim to study and compare several existing computational methods such as sample average approximation [1], scenario approximation [2], p-efficient points [3], and penalised convex difference [4] in practice.

Requirement: python programming skills (preferred), experience with ML libraries such as numpy, pytorch.

If interested, please send your CV and a transcript of your grades to mohammadsaeed.masiha@epfl.ch

References: [1] J. Luedtke and S. Ahmed. A sample approximation approach for optimization with probabilistic constraints. SIAM Journal on Optimization, 19:674–699, 2008. [2] G. C. Calafiore and M. C. Campi. The scenario approach to robust control design. IEEE Transactions on Automatic Control, 51(5):742–753, 2006. [3] D. Dentcheva, A. Pre ́kopa, and A. Ruszczynski. Concavity and efficient points of discrete distributions in probabilistic programming. Mathematical Programming, 89(1), 2000. [4] Laguel, Yassine, Jérôme Malick, and Wim Ackooij. "Chance constrained problems: a bilevel convex optimization perspective." arXiv preprint arXiv:2103.10832 (2021).