Summary of The Competition Complexity Of Prophet Inequalities with Correlations, by Tomer Ezra and Tamar Garbuz
The Competition Complexity of Prophet Inequalities with Correlations
by Tomer Ezra, Tamar Garbuz
First submitted to arxiv on: 10 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computer Science and Game Theory (cs.GT)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper explores the prophet inequality problem through a resource augmentation framework, focusing on scenarios where reward values are correlated. The goal is to determine how many additional rewards an online algorithm needs to approximate the maximum value of the original instance. While the independent reward case is well understood, this research extends that understanding to account for correlations among rewards. The results show that unlike in the independent case, the required number of additional rewards depends on the number of original rewards, and that block-threshold algorithms may require an infinite number of additional rewards when correlations are present. The paper develops asymptotically optimal algorithms for three scenarios: (1) where rewards arrive in blocks corresponding to different copies of the original instance; (2) where rewards across all copies are arbitrarily shuffled; and (3) where rewards arrive in blocks with pairwise independence within each block. The findings have implications for understanding the prophet inequality problem in correlated reward settings. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at a math problem called the prophet inequality problem, but makes it more complicated by mixing up the numbers that come out. The goal is to figure out how many extra rewards an online algorithm needs to get close to the best possible outcome. It’s like trying to predict what will happen in a game based on previous results. The researchers found that when the numbers are mixed up, you need even more extra rewards to get close than before. They came up with special algorithms for three different situations: when the numbers come in groups, when they’re all jumbled together, and when some groups have no connection to each other. This helps us understand how to solve this problem better. |
