Delegated Stochastic Probing

Authors Curtis Bechtel , Shaddin Dughmi



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Author Details

Curtis Bechtel
  • Department of Computer Science, University of Southern California, Los Angeles, USA
Shaddin Dughmi
  • Department of Computer Science, University of Southern California, Los Angeles, USA

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Curtis Bechtel and Shaddin Dughmi. Delegated Stochastic Probing. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 37:1-37:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ITCS.2021.37

Abstract

Delegation covers a broad class of problems in which a principal doesn't have the resources or expertise necessary to complete a task by themselves, so they delegate the task to an agent whose interests may not be aligned with their own. Stochastic probing describes problems in which we are tasked with maximizing expected utility by "probing" known distributions for acceptable solutions subject to certain constraints. In this work, we combine the concepts of delegation and stochastic probing into a single mechanism design framework which we term delegated stochastic probing. We study how much a principal loses by delegating a stochastic probing problem, compared to their utility in the non-delegated solution. Our model and results are heavily inspired by the work of Kleinberg and Kleinberg in "Delegated Search Approximates Efficient Search." Building on their work, we show that there exists a connection between delegated stochastic probing and generalized prophet inequalities, which provides us with constant-factor deterministic mechanisms for a large class of delegated stochastic probing problems. We also explore randomized mechanisms in a simple delegated probing setting, and show that they outperform deterministic mechanisms in some instances but not in the worst case.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic mechanism design
Keywords
  • Delegation
  • Mechanism Design
  • Algorithmic Game Theory

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References

  1. Marek Adamczyk and Michał Włodarczyk. Random order contention resolution schemes. In 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS), pages 790-801. IEEE, 2018. Google Scholar
  2. Ricardo Alonso and Niko Matouschek. Optimal delegation. The Review of Economic Studies, 75(1):259-293, 2008. Google Scholar
  3. Mark Armstrong and John Vickers. A model of delegated project choice. Econometrica, 78(1):213-244, 2010. Google Scholar
  4. Arash Asadpour and Hamid Nazerzadeh. Maximizing stochastic monotone submodular functions. Management Science, 62(8):2374-2391, 2016. Google Scholar
  5. Domagoj Bradac, Sahil Singla, and Goran Zuzic. (near) optimal adaptivity gaps for stochastic multi-value probing. arXiv preprint, 2019. URL: http://arxiv.org/abs/1902.01461.
  6. Chandra Chekuri, Jan Vondrák, and Rico Zenklusen. Submodular function maximization via the multilinear relaxation and contention resolution schemes. SIAM Journal on Computing, 43(6):1831-1879, 2014. Google Scholar
  7. Ning Chen, Nicole Immorlica, Anna R Karlin, Mohammad Mahdian, and Atri Rudra. Approximating matches made in heaven. In International Colloquium on Automata, Languages, and Programming, pages 266-278. Springer, 2009. Google Scholar
  8. Paul Dütting, Michal Feldman, Thomas Kesselheim, and Brendan Lucier. Prophet inequalities made easy: Stochastic optimization by pricing non-stochastic inputs. In 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), pages 540-551. IEEE, 2017. Google Scholar
  9. Moran Feldman, Ola Svensson, and Rico Zenklusen. Online contention resolution schemes. In Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms, pages 1014-1033. Society for Industrial and Applied Mathematics, 2016. Google Scholar
  10. Anupam Gupta and Viswanath Nagarajan. A stochastic probing problem with applications. In International Conference on Integer Programming and Combinatorial Optimization, pages 205-216. Springer, 2013. Google Scholar
  11. Anupam Gupta, Viswanath Nagarajan, and Sahil Singla. Algorithms and adaptivity gaps for stochastic probing. In Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms, pages 1731-1747. SIAM, 2016. Google Scholar
  12. Mohammad Taghi Hajiaghayi, Robert Kleinberg, and Tuomas Sandholm. Automated online mechanism design and prophet inequalities. In AAAI, volume 7, pages 58-65, 2007. Google Scholar
  13. Bengt Holmstrom. On the theory of delegation. Technical report, Discussion Paper, 1980. Google Scholar
  14. Bengt Robert Holmstrom. On Incentives and Control in Organizations. PhD thesis, Stanford University, 1978. Google Scholar
  15. Ali Khodabakhsh, Yuanzhe Liu, Emmanouil Pountourakis, Sam Taggart, and Yichi Zhang. Threshold policies for delegation. working paper, 2020. Google Scholar
  16. Jon Kleinberg and Robert Kleinberg. Delegated search approximates efficient search. In Proceedings of the 2018 ACM Conference on Economics and Computation, pages 287-302, 2018. Google Scholar
  17. Robert Kleinberg and Seth Matthew Weinberg. Matroid prophet inequalities. In Proceedings of the forty-fourth annual ACM Symposium on Theory of Computing, pages 123-136. ACM, 2012. Google Scholar
  18. Eugen Kováč and Tymofiy Mylovanov. Stochastic mechanisms in settings without monetary transfers: The regular case. Journal of Economic Theory, 144(4):1373-1395, 2009. Google Scholar
  19. Ulrich Krengel and Louis Sucheston. Semiamarts and finite values. Bulletin of the American Mathematical Society, 83(4):745-747, 1977. Google Scholar
  20. Ulrich Krengel and Louis Sucheston. On semiamarts, amarts, and processes with finite value. Probability on Banach spaces, 4:197-266, 1978. Google Scholar
  21. Euiwoong Lee and Sahil Singla. Optimal online contention resolution schemes via ex-ante prophet inequalities. In 26th Annual European Symposium on Algorithms (ESA 2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018. Google Scholar
  22. Brendan Lucier. An economic view of prophet inequalities. ACM SIGecom Exchanges, 16(1):24-47, 2017. Google Scholar
  23. Nahum D Melumad and Toshiyuki Shibano. Communication in settings with no transfers. The RAND Journal of Economics, pages 173-198, 1991. Google Scholar
  24. Tim Roughgarden. Twenty lectures on algorithmic game theory. Cambridge University Press, 2016. Google Scholar
  25. Ester Samuel-Cahn et al. Comparison of threshold stop rules and maximum for independent nonnegative random variables. the Annals of Probability, 12(4):1213-1216, 1984. Google Scholar
  26. Sahil Singla. Combinatorial Optimization Under Uncertainty: Probing and Stopping-Time Algorithms. PhD thesis, PhD thesis, Carnegie Mellon University, 2018. Google Scholar
  27. Martin L Weitzman. Optimal search for the best alternative. Econometrica: Journal of the Econometric Society, pages 641-654, 1979. Google Scholar
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