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Improved Prophet Inequalities for Combinatorial Welfare Maximization with (Approximately) Subadditive Agents

Author Hanrui Zhang



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Hanrui Zhang
  • Duke University, Durham, NC, USA

Acknowledgements

The author thanks Yuan Deng, Kamesh Munagala, and anonymous reviewers for helpful feedback.

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Hanrui Zhang. Improved Prophet Inequalities for Combinatorial Welfare Maximization with (Approximately) Subadditive Agents. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 82:1-82:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.ESA.2020.82

Abstract

We give a framework for designing prophet inequalities for combinatorial welfare maximization. Instantiated with different parameters, our framework implies (1) an O(log m / log log m)-competitive prophet inequality for subadditive agents, improving over the O(log m) upper bound via item pricing, (2) an O(D log m / log log m)-competitive prophet inequality for D-approximately subadditive agents, where D ∈ {1, … , m-1} measures the maximum number of items that complement each other, and (3) as a byproduct, an O(1)-competitive prophet inequality for submodular or fractionally subadditive (a.k.a. XOS) agents, matching the optimal ratio asymptotically. Our framework is computationally efficient given sample access to the prior and demand queries.

Subject Classification

ACM Subject Classification
  • Theory of computation → Stochastic approximation
  • Theory of computation → Algorithmic game theory and mechanism design
Keywords
  • Prophet Inequalities
  • Combinatorial Welfare Maximization
  • (Approximate) Subadditivity

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