Polymatroid Prophet Inequalities

  title={Polymatroid Prophet Inequalities},
  author={Paul D{\"u}tting and Robert D. Kleinberg},
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. 

Multiple-Choice Prophet Inequalities

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

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

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

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

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

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

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

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Single-Sample Prophet Inequalities via Greedy-Ordered Selection

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Automated Online Mechanism Design and Prophet Inequalities

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Approximating the stochastic knapsack problem: the benefit of adaptivity

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