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Duality in balance optimization subset selection

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Abstract

In this paper, we investigate a specific optimization problem that arises in the context of Balance Optimization Subset Selection (BOSS), which is an optimization framework for causal inference. Most BOSS problems can be formulated as mixed integer linear programs. By relaxing the integrality constraints so that fractional contributions of control units are permitted, a linear program (LP) is obtained. Properties of this LP and its dual are investigated and a sensitivity analysis is conducted to characterize how the objective value changes as the covariate values are perturbed.

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References

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Acknowledgements

The authors would like to thank the associate editor and two anonymous reviewers for their comments and suggestions which led to a considerably improved version of this paper.

The third author has been supported in part by the Air Force Office of Scientific Research under Grant No. FA9550-19-1-0106. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the United States Government, or the Air Force Office of Scientific Research.

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Author notes

  1. Hee Youn Kwon

    Present address: Northwestern Institute on Complex Systems (NICO), 600 Foster Street, Evanston, IL, 60208, USA

Authors and Affiliations

  1. Kellogg School of Management, Northwestern University, Evanston, IL, USA

    Hee Youn Kwon

  2. Department of Computer Science, University of Wisconsin-La Crosse, La Crosse, WI, USA

    Jason J. Sauppe

  3. Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Sheldon H. Jacobson

Authors
  1. Hee Youn Kwon
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  2. Jason J. Sauppe
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  3. Sheldon H. Jacobson
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Correspondence to Jason J. Sauppe.

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Kwon, H.Y., Sauppe, J.J. & Jacobson, S.H. Duality in balance optimization subset selection. Ann Oper Res 289, 277–289 (2020). https://doi.org/10.1007/s10479-020-03513-y

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  • DOI: https://doi.org/10.1007/s10479-020-03513-y

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