{"id":167501,"date":"2015-01-01T00:00:00","date_gmt":"2015-01-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/fast-algorithms-for-online-stochastic-convex-programming\/"},"modified":"2018-10-16T21:51:42","modified_gmt":"2018-10-17T04:51:42","slug":"fast-algorithms-for-online-stochastic-convex-programming","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/fast-algorithms-for-online-stochastic-convex-programming\/","title":{"rendered":"Fast algorithms for online stochastic convex programming"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We introduce the <em>online stochastic Convex Programming (CP) <\/em>problem, a very general version of stochastic online problems which allows arbitrary concave objectives and convex feasibility constraints. Many well-studied problems like online stochastic packing and covering, online stochastic matching with concave returns, etc. form a special case of online stochastic CP. We present fast algorithms for these problems, which achieve near-optimal regret guarantees <em>for both the i.i.d. and the random permutation models<\/em> of stochastic inputs. When applied to the special case online packing, our ideas yield a simpler and faster primal-dual algorithm for this well studied problem, which achieves the optimal <em>competitive ratio<\/em>. Our techniques make explicit the connection of primal-dual paradigm and online learning to online stochastic CP.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We introduce the online stochastic Convex Programming (CP) problem, a very general version of stochastic online problems which allows arbitrary concave objectives and convex feasibility constraints. Many well-studied problems like online stochastic packing and covering, online stochastic matching with concave returns, etc. form a special case of online stochastic CP. We present fast algorithms for [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13561,13556],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-167501","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-research-area-artificial-intelligence","msr-locale-en_us"],"msr_publishername":"SIAM - Society for Industrial and Applied Mathematics","msr_edition":"SODA 2015 (ACM-SIAM Symposium on Discrete 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