Optimistic robust optimization with applications to machine learning
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Authors
Norton, Matthew
Takeda, Akiko
Mafusalov, Alexander
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Date of Issue
2017-11-20
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Abstract
Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this paper, we explore an optimistic, or best-case view of uncertainty and show that it can be a fruitful approach. We show that these techniques can be used to address a wide variety of problems. First, we apply our methods in the context of robust linear programming, providing a method for reducing conservatism in intuitive ways that encode economically realistic modeling assumptions. Second, we look at problems in machine learning and find that this approach is strongly connected to the existing literature. Specifically, we provide a new interpretation for popular sparsity inducing non-convex regularization schemes. Additionally, we show that successful approaches for dealing with outliers and noise can be interpreted as optimistic robust optimization problems. Although many of the problems
resulting from our approach are non-convex, we find that DCA or DCA-like optimization approaches can be intuitive and e fficient.
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Description
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Department
Operations Research (OR)
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Naval Postgraduate School (U.S.)
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Format
34 p.
Citation
M. Norton, A. Takeda, Z. Mafusalov, "Optimistic robust optimization with applications to machine learning," arXiv:1711.07511v1 [stat.ML] 20 Nov 2017.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.