Tuesday, 13:15 - 13:40 h, Room: MA 042


Huan Xu
A distributional interpretation of robust optimization, with applications in machine learning

Coauthors: Constantine Caramanis, Shie Mannor


Motivated by data-driven decision making and sampling problems, we investigate probabilistic interpretations
of Robust Optimization (RO). We establish a connection between RO and Distributionally Robust Stochastic
Programming (DRSP), showing that the solution to any RO problem is also a solution to a DRSP problem.
Specically, we consider the case where multiple uncertain parameters belong to the same fixed dimensional
space, and find the set of distributions of the equivalent DRSP. The equivalence we derive enables us to construct
RO formulations for sampled problems (as in stochastic programming and machine learning) that are statistically
consistent, even when the original sampled problem is not. In the process, this provides a systematic approach for
tuning the uncertainty set. Applying this interpretation in machine learning, we showed that two widely used algorithms - SVM and Lasso are special cases of RO, and establish their consistency via the distributional interpretation.


Talk 1 of the invited session Tue.2.MA 042
"Advances in robust optimization" [...]
Cluster 20
"Robust optimization" [...]


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