{"id":158242,"date":"2009-07-01T00:00:00","date_gmt":"2009-07-01T00:00:00","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/msr-research-item\/maximizing-stochastic-monotone-submodular-functions\/"},"modified":"2018-10-16T19:57:58","modified_gmt":"2018-10-17T02:57:58","slug":"maximizing-stochastic-monotone-submodular-functions","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/maximizing-stochastic-monotone-submodular-functions\/","title":{"rendered":"Maximizing Stochastic Monotone Submodular Functions"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We study the problem of maximizing a stochastic monotone submodular function with respect to a matroid constraint. We study the adaptivity gap &#8211; the ratio between the values of optimal adaptive and non-adaptive policies &#8211; and show that it is equal to e\/(e-1) . This result implies that the benefit of adaptivity is bounded. We also study the myopic policy and show that it is a (1\/2)-approximation. Furthermore, when the matroid is uniform, approximation ratio of the myopic policy becomes 1-(1\/e) which is optimum.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We study the problem of maximizing a stochastic monotone submodular function with respect to a matroid constraint. We study the adaptivity gap &#8211; the ratio between the values of optimal adaptive and non-adaptive policies &#8211; and show that it is equal to e\/(e-1) . This result implies that the benefit of adaptivity is bounded. We 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