### Abstract

In a classical online decision problem, a decision-maker who is trying to maximize her value inspects a sequence of arriving items to learn their values (drawn from known distributions), and decides when to stop the process by taking the current item. The goal is to prove a "prophet inequality": that she can do approximately as well as a prophet with foreknowledge of all the values. In this work, we investigate this problem when the values are allowed to be correlated. Since non-trivial guarantees are impossible for arbitrary correlations, we consider a natural "linear" correlation structure introduced by Bateni et al. [ESA'15] as a generalization of the common-base value model of Chawla et al. [GEB'15]. A key challenge is that threshold-based algorithms, which are commonly used for prophet inequalities, no longer guarantee good performance for linear correlations. We relate this roadblock to another "augmentations" challenge that might be of independent interest: many existing prophet inequality algorithms are not robust to slight increase in the values of the arriving items. We leverage this intuition to prove bounds (matching up to constant factors) that decay gracefully with the amount of correlation of the arriving items. We extend these results to the case of selecting multiple items by designing a new $(1+o(1))$ approximation ratio algorithm that is robust to augmentations.

Original language | English (US) |
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Title of host publication | EC 2020 - Proceedings of the 21st ACM Conference on Economics and Computation |

Publisher | Association for Computing Machinery, Inc |

Pages | 159-185 |

Number of pages | 27 |

ISBN (Electronic) | 9781450379755 |

DOIs | |

State | Published - Jul 13 2020 |

Event | 21st ACM Conference on Economics and Computation, EC 2020 - Virtual, Online, Hungary Duration: Jul 13 2020 → Jul 17 2020 |

### Publication series

Name | EC 2020 - Proceedings of the 21st ACM Conference on Economics and Computation |
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### Conference

Conference | 21st ACM Conference on Economics and Computation, EC 2020 |
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Country | Hungary |

City | Virtual, Online |

Period | 7/13/20 → 7/17/20 |

### All Science Journal Classification (ASJC) codes

- Computer Science (miscellaneous)
- Economics and Econometrics
- Statistics and Probability
- Computational Mathematics

### Keywords

- online algorithms
- posted price mechanisms
- robust stopping time algorithms

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## Cite this

*EC 2020 - Proceedings of the 21st ACM Conference on Economics and Computation*(pp. 159-185). [3399452] (EC 2020 - Proceedings of the 21st ACM Conference on Economics and Computation). Association for Computing Machinery, Inc. https://doi.org/10.1145/3391403.3399452