_:n21f71838e43942f38d198d09f388ebdexb18
<http://schema.org/description>
"The secretary and the prophet inequality problems are central to the field of\nStopping Theory. Recently, there has been a lot of work in generalizing these\nmodels to multiple items because of their applications in mechanism design. The\nmost important of these generalizations are to matroids and to combinatorial\nauctions (extends bipartite matching). Kleinberg-Weinberg KW-STOC12 and\nFeldman et al. feldman2015combinatorial show that for adversarial\narrival order of random variables the optimal prophet inequalities give a\n1/2-approximation. For many settings, however, it's conceivable that the\narrival order is chosen uniformly at random, akin to the secretary problem. For\nsuch a random arrival model, we improve upon the 1/2-approximation and obtain\n(1-1/e)-approximation prophet inequalities for both matroids and\ncombinatorial auctions. This also gives improvements to the results of Yan\nyan2011mechanism and Esfandiari et al. esfandiari2015prophet who\nworked in the special cases where we can fully control the arrival order or\nwhen there is only a single item.\n  Our techniques are threshold based. We convert our discrete problem into a\ncontinuous setting and then give a generic template on how to dynamically\nadjust these thresholds to lower bound the expected total welfare."
<https://api.deepai.org/profile/thomas-kesselheim>