Document Open Access Logo

The Average-Value Allocation Problem

Authors Kshipra Bhawalkar , Zhe Feng , Anupam Gupta , Aranyak Mehta , David Wajc , Di Wang

PDF
Thumbnail PDF

File

LIPIcs.APPROX-RANDOM.2024.13.pdf
  • Filesize: 0.88 MB
  • 23 pages

Document Identifiers

Author Details

Kshipra Bhawalkar
  • Google Research, Mountain View, USA
Zhe Feng
  • Google Research, Mountain View, USA
Anupam Gupta
  • NYU & Google Research, New York City & Mountain View, USA
Aranyak Mehta
  • Google Research, Mountain View, USA
David Wajc
  • Technion, Haifa, Israel
Di Wang
  • Google Research, Mountain View, USA

Funding

  • Gupta, Anupam: Supported in part by NSF awards CCF-1955785 and CCF-2006953.
  • Wajc, David: Supported in part by a Taub Family Foundation "Leader in Science and Technology" fellowship. Work done while the author was visiting Google Research.

Cite AsGet BibTex

Kshipra Bhawalkar, Zhe Feng, Anupam Gupta, Aranyak Mehta, David Wajc, and Di Wang. The Average-Value Allocation Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 13:1-13:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.13

Abstract

We initiate the study of centralized algorithms for welfare-maximizing allocation of goods to buyers subject to average-value constraints. We show that this problem is NP-hard to approximate beyond a factor of e/(e-1), and provide a 4e/(e-1)-approximate offline algorithm. For the online setting, we show that no non-trivial approximations are achievable under adversarial arrivals. Under i.i.d. arrivals, we present a polytime online algorithm that provides a constant approximation of the optimal (computationally-unbounded) online algorithm. In contrast, we show that no constant approximation of the ex-post optimum is achievable by an online algorithm.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Online algorithms
Keywords
  • Resource allocation
  • return-on-spend constraint
  • approximation algorithm
  • online algorithm

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Gagan Aggarwal, Ashwinkumar Badanidiyuru, and Aranyak Mehta. Autobidding with constraints. In International Conference on Web and Internet Economics, pages 17-30. Springer, 2019. Google Scholar
  2. Shipra Agrawal and Nikhil R Devanur. Fast algorithms for online stochastic convex programming. In Proceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms, pages 1405-1424, 2014. Google Scholar
  3. Nima Anari, Rad Niazadeh, Amin Saberi, and Ali Shameli. Nearly optimal pricing algorithms for production constrained and laminar bayesian selection. In Proceedings of the 2019 ACM Conference on Economics and Computation, pages 91-92, 2019. Google Scholar
  4. Nick Arnosti and Will Ma. Tight guarantees for static threshold policies in the prophet secretary problem. Operations Research, 2022. Google Scholar
  5. Makis Arsenis and Robert Kleinberg. Individual fairness in prophet inequalities. In Proceedings of the 23rd ACM Conference on Economics and Computation, page 245, 2022. Google Scholar
  6. Yossi Azar, Andrei Z. Broder, Anna R. Karlin, and Eli Upfal. Balanced allocations. SIAM J. Comput., 29(1):180-200, 1999. Google Scholar
  7. Yossi Azar, Niv Buchbinder, TH Hubert Chan, Shahar Chen, Ilan Reuven Cohen, Anupam Gupta, Zhiyi Huang, Ning Kang, Viswanath Nagarajan, Joseph Naor, et al. Online algorithms for covering and packing problems with convex objectives. In 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS), pages 148-157. IEEE, 2016. Google Scholar
  8. Santiago Balseiro, Yuan Deng, Jieming Mao, Vahab Mirrokni, and Song Zuo. Robust auction design in the auto-bidding world. Advances in Neural Information Processing Systems, 34:17777-17788, 2021. Google Scholar
  9. Kshipra Bhawalkar, Zhe Feng, Anupam Gupta, Aranyak Mehta, David Wajc, and Di Wang. The average-value allocation problem, 2024. URL: https://arxiv.org/abs/2407.10401.
  10. Mark Braverman, Mahsa Derakhshan, and Antonio Molina Lovett. Max-weight online stochastic matching: Improved approximations against the online benchmark. In 23rd ACM Conference on economics and Computation, pages 967-985, 2022. Google Scholar
  11. Niv Buchbinder, Kamal Jain, and Joseph Seffi Naor. Online primal-dual algorithms for maximizing ad-auctions revenue. In European Symposium on Algorithms, pages 253-264, 2007. Google Scholar
  12. Niv Buchbinder, Kamal Jain, and Mohit Singh. Secretary problems via linear programming. Mathematics of Operations Research, 39(1):190-206, 2014. Google Scholar
  13. Gruia Calinescu, Chandra Chekuri, Martin Pal, and Jan Vondrák. Maximizing a monotone submodular function subject to a matroid constraint. SIAM Journal on Computing, 40(6):1740-1766, 2011. Google Scholar
  14. Deeparnab Chakrabarty and Gagan Goel. On the approximability of budgeted allocations and improved lower bounds for submodular welfare maximization and gap. SIAM Journal on Computing (SICOMP), 39(6):2189-2211, 2010. Google Scholar
  15. Yuan Deng, Jieming Mao, Vahab Mirrokni, and Song Zuo. Towards efficient auctions in an auto-bidding world. In Proceedings of the Web Conference 2021, WWW '21, pages 3965-3973. Association for Computing Machinery, 2021. Google Scholar
  16. Nikhil R. Devanur and Thomas P. Hayes. The adwords problem: online keyword matching with budgeted bidders under random permutations. In ACM Conference on Electronic Commerce, pages 71-78, 2009. URL: https://doi.org/10.1145/1566374.1566384.
  17. Nikhil R. Devanur and Kamal Jain. Online matching with concave returns. In Howard J. Karloff and Toniann Pitassi, editors, Proceedings of the 44th Symposium on Theory of Computing Conference, STOC 2012, New York, NY, USA, May 19 - 22, 2012, pages 137-144. ACM, 2012. URL: https://doi.org/10.1145/2213977.2213992.
  18. Nikhil R. Devanur, Kamal Jain, Balasubramanian Sivan, and Christopher A. Wilkens. Near optimal online algorithms and fast approximation algorithms for resource allocation problems. In ACM Conference on Electronic Commerce, pages 29-38, 2011. URL: https://doi.org/10.1145/1993574.1993581.
  19. Tomer Ezra, Michal Feldman, Nick Gravin, and Zhihao Gavin Tang. “who is next in line?” on the significance of knowing the arrival order in bayesian online settings. In Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 3759-3776, 2023. Google Scholar
  20. Auto-bidding products support page. https://www.facebook.com/business/help/1619591734742116, 2022. Accessed: 2023-07-12.
  21. Uriel Feige. A threshold of ln n for approximating set cover. Journal of the ACM (JACM), 45(4):634-652, 1998. Google Scholar
  22. Jon Feldman, Monika Henzinger, Nitish Korula, Vahab S. Mirrokni, and Clifford Stein. Online stochastic packing applied to display ad allocation. In ESA (1), pages 182-194, 2010. URL: https://doi.org/10.1007/978-3-642-15775-2_16.
  23. Lisa Fleischer, Michel X Goemans, Vahab S Mirrokni, and Maxim Sviridenko. Tight approximation algorithms for maximum separable assignment problems. Mathematics of Operations Research, 36(3):416-431, 2011. Google Scholar
  24. Negin Golrezaei, Ilan Lobel, and Renato Paes Leme. Auction design for roi-constrained buyers. In Proceedings of the Web Conference 2021, WWW '21, pages 3941-3952, 2021. Google Scholar
  25. Auto-bidding products support page. https://support.google.com/google-ads/answer/2979071, 2022. Accessed: 2023-07-12.
  26. Anupam Gupta and Marco Molinaro. How the experts algorithm can help solve LPs online. Math. Oper. Res., 41(4):1404-1431, 2016. Google Scholar
  27. Johan Håstad. Clique is hard to approximate within n^1-ε. In Proceedings of 37th Conference on Foundations of Computer Science, pages 627-636, 1996. Google Scholar
  28. Zhiyi Huang, Qiankun Zhang, and Yuhao Zhang. Adwords in a panorama. In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), pages 1416-1426, 2020. Google Scholar
  29. Kristen Kessel, Ali Shameli, Amin Saberi, and David Wajc. The stationary prophet inequality problem. In Proceedings of the 23rd ACM Conference on Economics and Computation, pages 243-244, 2022. Google Scholar
  30. Thomas Kesselheim, Klaus Radke, Andreas Tönnis, and Berthold Vöcking. Primal beats dual on online packing lps in the random-order model. SIAM J. Comput., 47(5):1939-1964, 2018. Google Scholar
  31. Aranyak Mehta. Auction design in an auto-bidding setting: Randomization improves efficiency beyond VCG. In Proceedings of the ACM Web Conference 2022, pages 173-181, 2022. Google Scholar
  32. Aranyak Mehta, Amin Saberi, Umesh Vazirani, and Vijay Vazirani. Adwords and generalized online matching. Journal of the ACM (J.ACM), 54(5):22, 2007. Google Scholar
  33. Joseph (Seffi) Naor, Aravind Srinivasan, and David Wajc. Online dependent rounding schemes. arXiv preprint arXiv:2301.08680, 2023. Google Scholar
  34. Christos Papadimitriou, Tristan Pollner, Amin Saberi, and David Wajc. Online stochastic max-weight bipartite matching: Beyond prophet inequalities. In Proceedings of the 22nd ACM Conference on Economics and Computation, pages 763-764, 2021. Google Scholar
  35. Sebastian Perez-Salazar, Mohit Singh, and Alejandro Toriello. The iid prophet inequality with limited flexibility. arXiv preprint arXiv:2210.05634, 2022. Google Scholar
  36. David Zuckerman. Linear degree extractors and the inapproximability of max clique and chromatic number. In Proceedings of the thirty-eighth annual ACM symposium on Theory of computing, pages 681-690, 2006. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact