# Polymatroid Prophet Inequalities

@article{Dtting2015PolymatroidPI, title={Polymatroid Prophet Inequalities}, author={Paul D{\"u}tting and Robert D. Kleinberg}, journal={ArXiv}, year={2015}, volume={abs/1307.5299} }

Prophet inequalities bound the reward of an online algorithm—or gambler—relative to the optimum offline algorithm—the prophet—in settings that involve making selections from a sequence of elements whose order is chosen adversarially but whose weights are random. The goal is to maximize total weight.

## 51 Citations

### Multiple-Choice Prophet Inequalities

- Mathematics
- 2016

The well-established Prophet Inequality concerns an online algorithm that observes a sequence of random variables X1, . . . , Xn with known distribution in order, and must decide, when it observes…

### Prophet Inequalities via the Expected Competitive Ratio

- EconomicsArXiv
- 2022

We consider prophet inequalities under general downward-closed constraints. In a prophet inequality problem, a decision-maker sees a series of online elements and needs to decide immediately and…

### Prophet Secretary for Combinatorial Auctions and Matroids

- MathematicsSODA
- 2018

The secretary and the prophet inequality problems are central to the field of Stopping Theory and this work improves upon the $1/2$-approximation and obtains $(1-1/e)$- approximation prophet inequalities for both matroids and combinatorial auctions.

### An O(log log m) Prophet Inequality for Subadditive Combinatorial Auctions

- Computer Science2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
- 2020

A simple and incentive compatible mechanism based on posted prices that achieves an O(log log m) approximation to the optimal revenue for subadditive valuations under an item-independence assumption is constructed.

### An Improved Prophet Inequality for Combinatorial Welfare Maximization with Subadditive Agents

- Economics, Mathematics
- 2019

We give an O(logm/ log logm)-competitive prophet inequality for combinatorial welfare maximization with subadditive agents, improving over the O(logm) upper bound. Our policy is computationally…

### Prophet Inequalities Made Easy: Stochastic Optimization by Pricing Non-Stochastic Inputs

- Computer Science, Mathematics2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
- 2017

This work presents a general framework for stochastic online maximization problems with combinatorial feasibility constraints, and highlights a surprising connection between the smoothness framework for bounding the price of anarchy of mechanisms and the framework.

### Query Efficient Prophet Inequality with Unknown I.I.D. Distributions

- Computer ScienceArXiv
- 2022

A new model is proposed in which the algorithm has access to an oracle that answers quantile queries about the distribution and the extent to which it can use a small number of queries to achieve good competitive ratios is studied.

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

- MathematicsESA
- 2020

A framework for designing prophet inequalities for combinatorial welfare maximization and an O(1)-competitive prophet inequality for subadditive agents, matching the optimal ratio asymptotically is given.

### Single-Sample Prophet Inequalities via Greedy-Ordered Selection

- MathematicsSODA
- 2022

This work develops an intuitive and versatile greedy-based technique that yields SSPIs directly rather than through the reduction to OOSs, and analyzes the power and limitations of different SSPI approaches by providing a partial converse to the reduction from S SPI to O OS given by Azar et al.

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