{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T07:43:28Z","timestamp":1723016608604},"publisher-location":"California","reference-count":0,"publisher":"International Joint Conferences on Artificial Intelligence Organization","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p>We give polynomial time algorithms for escaping from high-dimensional saddle points under a moderate number of constraints. Given gradient access to a smooth function, we show that (noisy) gradient descent methods can escape from saddle points under a logarithmic number of inequality constraints. While analogous results exist for unconstrained and equality-constrained problems, we make progress on the major open question of convergence to second-order stationary points in the case of inequality constraints, without reliance on NP-oracles or altering the definitions to only account for certain constraints. Our results hold for both regular and stochastic gradient descent.<\/jats:p>","DOI":"10.24963\/ijcai.2023\/383","type":"proceedings-article","created":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T04:31:30Z","timestamp":1691728290000},"page":"3442-3450","source":"Crossref","is-referenced-by-count":0,"title":["HOUDINI: Escaping from Moderately Constrained Saddles"],"prefix":"10.24963","author":[{"given":"Dmitrii","family":"Avdiukhin","sequence":"first","affiliation":[{"name":"Indiana University, Bloomington"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Grigory","family":"Yaroslavtsev","sequence":"additional","affiliation":[{"name":"George Mason University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"10584","event":{"number":"32","sponsor":["International Joint Conferences on Artificial Intelligence Organization (IJCAI)"],"acronym":"IJCAI-2023","name":"Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}","start":{"date-parts":[[2023,8,19]]},"theme":"Artificial Intelligence","location":"Macau, SAR China","end":{"date-parts":[[2023,8,25]]}},"container-title":["Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence"],"original-title":[],"deposited":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T04:47:27Z","timestamp":1691729247000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ijcai.org\/proceedings\/2023\/383"}},"subtitle":[],"proceedings-subject":"Artificial Intelligence Research Articles","short-title":[],"issued":{"date-parts":[[2023,8]]},"references-count":0,"URL":"https:\/\/doi.org\/10.24963\/ijcai.2023\/383","relation":{},"subject":[],"published":{"date-parts":[[2023,8]]}}}