Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
169 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Combinatorial Stationary Prophet Inequalities (2312.08245v2)

Published 13 Dec 2023 in cs.GT and cs.DS

Abstract: Numerous papers have studied the tension between thickening and clearing a market in (uncertain, online) long-time horizon Markovian settings. In particular, (Aouad and Sarita{\c{c}} EC'20, Collina et al. WINE'20, Kessel et al. EC'22) studied what the latter referred to as the Stationary Prophet Inequality Problem, due to its similarity to the classic finite-time horizon prophet inequality problem. These works all consider unit-demand buyers. Mirroring the long line of work on the classic prophet inequality problem subject to combinatorial constraints, we initiate the study of the stationary prophet inequality problem subject to combinatorially-constrained buyers. Our results can be summarized succinctly as unearthing an algorithmic connection between contention resolution schemes (CRS) and stationary prophet inequalities. While the classic prophet inequality problem has a tight connection to online CRS (Feldman et al. SODA'16, Lee and Singla ESA'18), we show that for the stationary prophet inequality problem, offline CRS play a similarly central role. We show that, up to small constant factors, the best (ex-ante) competitive ratio achievable for the combinatorial prophet inequality equals the best possible balancedness achievable by offline CRS for the same combinatorial constraints.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (43)
  1. Improved approximation algorithms for stochastic matching. In Algorithms-ESA 2015: 23rd Annual European Symposium, Patras, Greece, September 14-16, 2015, Proceedings. Springer, 1–12.
  2. Price of correlations in stochastic optimization. Operations Research 60, 1, 150–162.
  3. Online prophet-inequality matching with applications to ad allocation. In Proceedings of the 13th ACM Conference on Electronic Commerce (EC). 18–35.
  4. Nearly optimal pricing algorithms for production constrained and laminar bayesian selection. In EC (2019). 91–92.
  5. Dynamic stochastic matching under limited time. In Proceedings of the 21st ACM Conference on Economics and Computation (EC). 789–790.
  6. Tight guarantees for static threshold policies in the prophet secretary problem. Operations Research.
  7. Improved bounds in stochastic matching and optimization. Algorithmica 80, 3225–3252.
  8. Delegated pandora’s box. In Proceedings of the 23rd ACM Conference on Economics and Computation. 666–693.
  9. On the pathwise comparison of jump processes driven by stochastic intensities. Mathematische Nachrichten 167, 1, 21–42.
  10. Max-weight online stochastic matching: Improved approximations against the online benchmark. In EC (2022). To appear.
  11. Maximizing a monotone submodular function subject to a matroid constraint. SIAM Journal on Computing (SICOMP) 40, 6, 1740–1766.
  12. Multi-budgeted matchings and matroid intersection via dependent rounding. In Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). 1080–1097.
  13. Dynamic weighted matching with heterogeneous arrival and departure rates. In Proceedings of the 16th Conference on Web and Internet Economics (WINE). 17–30.
  14. Dughmi, S. 2020. The outer limits of contention resolution on matroids and connections to the secretary problem. In Proceedings of the 47th International Colloquium on Automata, Languages and Programming (ICALP). 42:1–42:18.
  15. On sparsification of stochastic packing problems. In Proceedings of the 50th International Colloquium on Automata, Languages and Programming (ICALP). 51:1–51:17.
  16. Prophet inequalities made easy: Stochastic optimization by pricing nonstochastic inputs. SIAM Journal on Computing (SICOMP) 49, 3, 540–582.
  17. Prophet secretary against the online optimal. In Proceedings of the 24th ACM Conference on Economics and Computation (EC).
  18. An o (log log m) prophet inequality for subadditive combinatorial auctions. In Proceedings of the 61st Symposium on Foundations of Computer Science (FOCS). 306–317.
  19. Polymatroid prophet inequalities. In Proceedings of the 23rd Annual European Symposium on Algorithms (ESA). Springer, 437–449.
  20. Online stochastic max-weight matching: prophet inequality for vertex and edge arrival models. In Proceedings of the 21st ACM Conference on Economics and Computation (EC). 769–787.
  21. Feige, U. 2006. On maximizing welfare when utility functions are subadditive. In Proceedings of the thirty-eighth annual ACM symposium on Theory of computing. 41–50.
  22. Online contention resolution schemes. In Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). 1014–1033.
  23. Goldreich, O. 2017. Introduction to property testing. Cambridge University Press.
  24. Prophet inequality for bipartite matching: Merits of being simple and non adaptive. In Proceedings of the 20th ACM Conference on Economics and Computation (EC). 93–109.
  25. Automated online mechanism design and prophet inequalities. In Proceedings of the 22nd AAAI Conference on Artificial Intelligence (AAAI). 58–65.
  26. The stationary prophet inequality problem. In Proceedings of the 23rd ACM Conference on Economics and Computation (EC). 243–244.
  27. Matroid prophet inequalities and applications to multi-dimensional mechanism design. Games and Economic Behavior 113, 97–115.
  28. Semiamarts and finite values. Bulletin of the American Mathematical Society 83, 4, 745–747.
  29. On semiamarts, amarts, and processes with finite value. Probability on Banach spaces 4, 197–266.
  30. Optimal online contention resolution schemes via ex-ante prophet inequalities. In Proceedings of the 26th Annual European Symposium on Algorithms (ESA).
  31. Online dependent rounding schemes. arXiv preprint arXiv:2301.08680.
  32. Prophet inequalities vs. approximating optimum online. In WINE (2018). 356–374.
  33. Online stochastic max-weight bipartite matching: Beyond prophet inequalities. In EC (2021). 763–764.
  34. Improved online contention resolution for matchings and applications to the gig economy. In Proceedings of the 23rd ACM Conference on Economics and Computation. 321–322.
  35. Ross, S. M. 1995. Stochastic processes. John Wiley & Sons.
  36. Rubinstein, A. 2016. Beyond matroids: Secretary problem and prophet inequality with general constraints. In Proceedings of the 48th Annual ACM Symposium on Theory of Computing (STOC). 324–332.
  37. Combinatorial prophet inequalities. In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM, 1671–1687.
  38. Vondrák, J. 2007. Submodularity in combinatorial optimization. Ph.D. thesis.
  39. Vondrák, J. 2008. Optimal approximation for the submodular welfare problem in the value oracle model. In Proceedings of the 40th Annual ACM Symposium on Theory of Computing (STOC). 67–74.
  40. Vondrák, J. 2013. Symmetry and approximability of submodular maximization problems. SIAM Journal on Computing (SICOMP) 42, 1, 265–304.
  41. Submodular function maximization via the multilinear relaxation and contention resolution schemes. In Proceedings of the forty-third annual ACM symposium on Theory of computing. 783–792.
  42. Wolff, R. W. 1982. Poisson arrivals see time averages. Operations Research 30, 2, 223–231.
  43. Zhang, H. 2022. Improved prophet inequalities for combinatorial welfare maximization with (approximately) subadditive agents. J. Comput. Syst. Sci. 123, 143–156.
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