_:n21f71838e43942f38d198d09f388ebdexb24
<http://schema.org/description>
"Prophet inequalities compare the expected performance of an online algorithm\nfor a stochastic optimization problem to the expected optimal solution in\nhindsight. They are a major alternative to classic worst-case competitive\nanalysis, of particular importance in the design and analysis of simple\n(posted-price) incentive compatible mechanisms with provable approximation\nguarantees.\n  A central open problem in this area concerns subadditive combinatorial\nauctions. Here n agents with subadditive valuation functions compete for the\nassignment of m items. The goal is to find an allocation of the items that\nmaximizes the total value of the assignment. The question is whether there\nexists a prophet inequality for this problem that significantly beats the best\nknown approximation factor of O(log m).\n  We make major progress on this question by providing an O(loglog m)\nprophet inequality. Our proof goes through a novel primal-dual approach. It is\nalso constructive, resulting in an online policy that takes the form of static\nand anonymous item prices that can be computed in polynomial time given\nappropriate query access to the valuations. As an application of our approach,\nwe construct a simple and incentive compatible mechanism based on posted prices\nthat achieves an O(loglog m) approximation to the optimal revenue for\nsubadditive valuations under an item-independence assumption."
<https://api.deepai.org/profile/thomas-kesselheim>