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Structured Robust Submodular Maximization: Offline and Online Algorithms

Author

Listed:
  • Alfredo Torrico

    (Polytechnique Montréal, University of Montreal, Montreal, Quebec H3T 1J4, Canada)

  • Mohit Singh

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Sebastian Pokutta

    (Berlin Institute of Technology, 10623 Berlin, Germany; Zuse Institute Berlin, 14195 Berlin, Germany)

  • Nika Haghtalab

    (Department of Computer Science, Cornell University, Ithaca, New York 14853)

  • Joseph (Seffi) Naor

    (Technion—Israel Institute of Technology, Haifa 3200003, Israel)

  • Nima Anari

    (Computer Science Department, Stanford University, Stanford, California 94305)

Abstract

Constrained submodular function maximization has been used in subset selection problems such as selection of most informative sensor locations. Although these models have been quite popular, the solutions obtained via this approach are unstable to perturbations in data defining the submodular functions. Robust submodular maximization has been proposed as a richer model that aims to overcome this discrepancy as well as increase the modeling scope of submodular optimization. In this work, we consider robust submodular maximization with structured combinatorial constraints and give efficient algorithms with provable guarantees. Our approach is applicable to constraints defined by single or multiple matroids and knapsack as well as distributionally robust criteria. We consider both the offline setting where the data defining the problem are known in advance and the online setting where the input data are revealed over time. For the offline setting, we give a general (nearly) optimal bicriteria approximation algorithm that relies on new extensions of classical algorithms for submodular maximization. For the online version of the problem, we give an algorithm that returns a bicriteria solution with sublinear regret. Summary of Contribution: Constrained submodular maximization is one of the core areas in combinatorial optimization with a wide variety of applications in operations research and computer science. Over the last decades, both communities have been interested on the design and analysis of new algorithms with provable guarantees. Sensor location, influence maximization and data summarization are some of the applications of submodular optimization that lie at the intersection of the aforementioned communities. Particularly, our work focuses on optimizing several submodular functions simultaneously. We provide new insights and algorithms to the offline and online variants of the problem which significantly expand the related literature. At the same time, we provide a computational study that supports our theoretical results.

Suggested Citation

  • Alfredo Torrico & Mohit Singh & Sebastian Pokutta & Nika Haghtalab & Joseph (Seffi) Naor & Nima Anari, 2021. "Structured Robust Submodular Maximization: Offline and Online Algorithms," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1590-1607, October.
  • Handle: RePEc:inm:orijoc:v:33:y:2021:i:4:p:1590-1607
    DOI: 10.1287/ijoc.2020.0998
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    References listed on IDEAS

    as
    1. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions - 1," LIDAM Reprints CORE 334, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. A.A. Ageev & M.I. Sviridenko, 2004. "Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 307-328, September.
    3. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions," LIDAM Reprints CORE 341, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Wolsey, L.A., 1982. "An analysis of the greedy algorithm for the submodular set covering problem," LIDAM Reprints CORE 519, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

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