Distributionally robust submodular maximization
Name
1802.05249.pdf
Description
Submitted version
Size
725.46 KB
Format
Adobe PDF
Checksum (MD5)
78100c76ce9d7164ee99a8abe0c8a1ef
Author(s)
Staib, Matthew
Wilder, B
Jegelka, Stefanie Sabrina
Date Issued
April 2019
Journal
22nd International Conference on Artificial Intelligence and Statistics
Publisher
MLResearchPress
Citation
Staib, Matthew et al. "Distributionally robust submodular maximization." 22nd International Conference on Artificial Intelligence and Statistics, April 2019, Naha, Okinawa, Japan, MLResearchPress, April 2019. © 2019 by the author(s)
Version
Original manuscript
Abstract
Submodular functions have applications throughout machine learning, but in many settings, we do not have direct access to the underlying function f. We focus on stochastic functions that are given as an expectation of functions over a distribution P. In practice, we often have only a limited set of samples fi from P. The standard approach indirectly optimizes f by maximizing the sum of fi. However, this ignores generalization to the true (unknown) distribution. In this paper, we achieve better performance on the actual underlying function f by directly optimizing a combination of bias and variance. Algorithmically, we accomplish this by showing how to carry out distributionally robust optimization (DRO) for submodular functions, providing efficient algorithms backed by theoretical guarantees which leverage several novel contributions to the general theory of DRO. We also show compelling empirical evidence that DRO improves generalization to the unknown stochastic submodular function.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
http://proceedings.mlr.press/v89/staib19a.html
