Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
157 tokens/sec
GPT-4o
43 tokens/sec
Gemini 2.5 Pro Pro
43 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
47 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Threshold Policies with Tight Guarantees for Online Selection with Convex Costs (2310.06166v2)

Published 9 Oct 2023 in cs.GT and cs.DS

Abstract: This paper provides threshold policies with tight guarantees for online selection with convex cost (OSCC). In OSCC, a seller wants to sell some asset to a sequence of buyers with the goal of maximizing her profit. The seller can produce additional units of the asset, but at non-decreasing marginal costs. At each time, a buyer arrives and offers a price. The seller must make an immediate and irrevocable decision in terms of whether to accept the offer and produce/sell one unit of the asset to this buyer. The goal is to develop an online algorithm that selects a subset of buyers to maximize the seller's profit, namely, the total selling revenue minus the total production cost. Our main result is the development of a class of simple threshold policies that are logistically simple and easy to implement, but have provable optimality guarantees among all deterministic algorithms. We also derive a lower bound on competitive ratios of randomized algorithms and prove that the competitive ratio of our threshold policy asymptotically converges to this lower bound when the total production output is sufficiently large. Our results generalize and unify various online search, pricing, and auction problems, and provide a new perspective on the impact of non-decreasing marginal costs on real-world online resource allocation problems.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (41)
  1. Admission control to minimize rejections and online set cover with repetitions. ACM Trans. Algorithms, 6(1), dec 2010.
  2. Minimum-cost network design with (dis)economies of scale. SIAM Journal on Computing, 45(1):49–66, 2016.
  3. Secretary and online matching problems with machine learned advice. In Proceedings of the 34th International Conference on Neural Information Processing Systems, NIPS’20, Red Hook, NY, USA, 2020. Curran Associates Inc.
  4. Y. Azar et al. Online algorithms for covering and packing problems with convex objectives. In Proocedings of the 57th Annual Symposium on Foundations of Computer Science (FOCS ’16), pages 148–157, Oct. 2016.
  5. Regularized online allocation problems: Fairness and beyond. In Marina Meila and Tong Zhang, editors, Proceedings of the 38th International Conference on Machine Learning, volume 139 of Proceedings of Machine Learning Research, pages 630–639. PMLR, 18–24 Jul 2021.
  6. The primal-dual method for learning augmented algorithms. In H. Larochelle, M. Ranzato, R. Hadsell, M.F. Balcan, and H. Lin, editors, Advances in Neural Information Processing Systems, volume 33, pages 20083–20094. Curran Associates, Inc., 2020.
  7. Incentive compatible multi unit combinatorial auctions. In Proceedings of the 9th Conference on Theoretical Aspects of Rationality and Knowledge, TARK ’03, pages 72–87, New York, NY, USA, 2003. ACM.
  8. Welfare and profit maximization with production costs. In Proceedings of the 52nd Annual Symposium on Foundations of Computer Science (FOCS ’11), pages 77–86, 2011.
  9. Convex Analysis and Nonlinear Optimization. CMS Books in Mathematics. Springer New York, New York, NY, 2006.
  10. Niv Buchbinder and R. Gonen. Incentive compatible multi-unit combinatorial auctions: A primal dual approach. Algorithmica, 72:167–190, 2015.
  11. Improved bounds for online routing and packing via a primal-dual approach. In Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS ’06), Oct 2006.
  12. Online Primal-Dual Algorithms for Covering and Packing. Mathematics of Operations Research, 34(2):270–286, May 2009.
  13. The design of competitive online algorithms via a primal-dual approach. Found. Trends Theor. Comput. Sci., 3(2-3):93–263, February 2009.
  14. Optimal online algorithms for one-way trading and online knapsack problems: A unified competitive analysis. In 2020 59th IEEE Conference on Decision and Control (CDC), pages 1064–1069, 2020.
  15. Design of price mechanisms for network resource allocation via price of anarchy. Mathematical Programming, 131(1):333–364, Feb 2012.
  16. The Adwords problem: Online keyword matching with budgeted bidders under random permutations. In Proceedings of the 10th ACM Conference on Electronic Commerce (EC ’09), 2009.
  17. Online matching with concave returns. In Proceedings of the Forty-fourth Annual ACM Symposium on Theory of Computing, STOC ’12, pages 137–144, New York, NY, USA, 2012. ACM.
  18. Optimal search and one-way trading online algorithms. Algorithmica, 30(1):101–139, 2001.
  19. Online mechanism design for electric vehicle charging. In The 10th International Conference on Autonomous Agents and Multiagent Systems (AAMAS ’11), page 811–818, 2011.
  20. Random-Order Models. Chapter 11 – Beyond the Worst-Case Analysis of Algorithms. Cambridge University Press, 2021.
  21. Welfare maximization with production costs: A primal dual approach. Games and Economic Behavior, 118(C):648–667, 2019.
  22. Optimal control of admission in service in a queue with impatience and setup costs. Performance Evaluation, 144:102134, 2020.
  23. Online knapsack with frequency predictions. In M. Ranzato, A. Beygelzimer, Y. Dauphin, P.S. Liang, and J. Wortman Vaughan, editors, Advances in Neural Information Processing Systems, volume 34, pages 2733–2743. Curran Associates, Inc., 2021.
  24. Online selection problems against constrained adversary. In Marina Meila and Tong Zhang, editors, Proceedings of the 38th International Conference on Machine Learning, volume 139 of Proceedings of Machine Learning Research, pages 5002–5012. PMLR, 18–24 Jul 2021.
  25. A scalable network resource allocation mechanism with bounded efficiency loss. IEEE Journal on Selected Areas in Communications, 24(5):992–999, 2006.
  26. An optimal deterministic algorithm for online b-matching. Theor. Comput. Sci., 233(1-2):319–325, February 2000.
  27. Robert Kleinberg. A multiple-choice secretary algorithm with applications to online auctions. In Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’05, page 630–631, USA, 2005. Society for Industrial and Applied Mathematics.
  28. Competitive online optimization under inventory constraints. Proc. ACM Meas. Anal. Comput. Syst. (SIGMETRICS ’19), 3(1), March 2019.
  29. Optimal algorithms for k𝑘kitalic_k-search with application in option pricing. Algorithmica, 55(2):311–328, 2009.
  30. George S. Lueker. Average-case analysis of off-line and on-line knapsack problems. In Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’95, pages 179–188, USA, 1995. Society for Industrial and Applied Mathematics.
  31. Algorithms for online matching, assortment, and pricing with tight weight-dependent competitive ratios. Operations Research, 68(6):1787–1803, 2020.
  32. A. Marchetti-Spaccamela and C. Vercellis. Stochastic on-line knapsack problems. Mathematical Programming, 68(1):73–104, January 1995.
  33. Adwords and generalized online matching. Journal of ACM, 54(5), October 2007.
  34. Algorithmic Game Theory. Cambridge University Press, 2007.
  35. Pareto-optimal learning-augmented algorithms for online conversion problems. In Annual Conference on Neural Information Processing Systems 2021 (NeurIPS ’21), December 6-14, 2021, pages 10339–10350, 2021.
  36. Competitive algorithms for the online multiple knapsack problem with application to electric vehicle charging. Proc. ACM Meas. Anal. Comput. Syst. (SIGMETRICS ’21), 4(3), November 2020.
  37. Mechanism design for online resource allocation: A unified approach. Proc. ACM Meas. Anal. Comput. Syst. (SIGMETRICS ’20), 4(2), June 2020.
  38. Power-aware speed scaling in processor sharing systems. In IEEE INFOCOM 2009, pages 2007–2015, 2009.
  39. Online auctions in iaas clouds: Welfare and profit maximization with server costs. In Proceedings of the 2015 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems (SIGMETRICS ’15), pages 3–15, 2015.
  40. Optimal posted prices for online cloud resource allocation. Proc. ACM Meas. Anal. Comput. Syst. (SIGMETRICS ’17), 1(1), June 2017.
  41. Budget constrained bidding in keyword auctions and online knapsack problems. In Proceedings of the 17th International Conference on World Wide Web (WWW ’08). ACM, 2008.
Citations (2)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now