The University of Arizona
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Computationally Efficient approximations for Distributionally Robust Optimization

Statistics GIDP Colloquium

Computationally Efficient approximations for Distributionally Robust Optimization
Series: Statistics GIDP Colloquium
Location: ENR2 S395
Presenter: Jianqiang Cheng, Systems and Industrial Engineering, University of Arizona

Distributionally robust optimization (DRO) has gained increasing popularity because it offers a way to overcome the conservativeness of robust optimization without requiring the specificity of stochastic optimization. On the computational side, many practical DRO instances can be equivalently (or approximately) formulated as semidefinite programming (SDP) problems via conic duality of the moment problem. However, despite being theoretically solvable in polynomial time, SDP problems in practice are computationally challenging and quickly become intractable with increasing problem size. In this talk, we adopt the principal component analysis (PCA) approach to solve DRO problems with different types of ambiguity sets. We show that the PCA approximation yields a relaxation of the original problem and derive theoretical bounds on the gap between the original problem and its PCA approximation. Furthermore, an extensive numerical study shows the strength of the proposed approximation method in terms of solution quality and runtime.

(Refreshments will be served.)