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DFO: A Robust Framework for Data-driven Decision-making with Outliers

Nan Jiang (jnan97***at***vt.edu)
Weijun Xie (wxie***at***vt.edu)

Abstract: This work studies Distributionally Favorable Optimization (DFO), which seeks the best decision of a data-driven stochastic program under the most favorable distribution from a distributional family. When a stochastic program contains either endogenous or exogenous outliers, the commonly-used Distributionally Robust Optimization (DRO) models tend to over-emphasize the unrealistic scenarios, and cause non-robust misleading or even infeasible decisions. On the contrary, DFO can significantly mitigate the effects of outliers and has not yet been well studied. Thus, this paper fills the gap and shows that DFO recovers many robust statistics and can be truly ``robust" in the presence of outliers. While being NP-hard in general, many DFO models can be mixed-integer convex programming representable. We further propose a notion of decision outlier robustness to properly select a DFO framework for the data-driven optimization with outliers and extend the proposed DFO frameworks to solve two-stage stochastic programs without relatively complete recourse. The numerical study confirms the promising of the proposed frameworks.

Keywords: Distributionally Favorable Optimization; Distributionally Robust Optimization; Robust Statistics; Tractability; Mixed-Integer Convex Programming Representability

Category 1: Stochastic Programming

Category 2: Robust Optimization

Citation: Jiang, N., Xie, W. (2021). DFO: A Robust Framework for Data-driven Decision-making with Outliers. Available at Optimization Online.

Download: [PDF]

Entry Submitted: 10/21/2021
Entry Accepted: 10/21/2021
Entry Last Modified: 11/18/2021

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