{"type":"ScholarlyArticle","title":"Efficient Convex Optimization Requires Superlinear Memory (Extended Abstract)","authors":[{"name":"Annie Marsden","slug":"annie-marsden","given":"Annie","family":"Marsden","affiliation":"Stanford University"},{"name":"Vatsal Sharan","slug":"vatsal-sharan","given":"Vatsal","family":"Sharan","affiliation":"University of Southern California"},{"name":"Aaron Sidford","slug":"aaron-sidford","given":"Aaron","family":"Sidford","affiliation":"Stanford University"},{"name":"Gregory Valiant","slug":"gregory-valiant","given":"Gregory","family":"Valiant","affiliation":"Stanford University"}],"abstract":"Minimizing a convex function with access to a first order oracle---that returns the function evaluation and (sub)gradient at a query point---is a canonical optimization problem and a fundamental primitive in machine learning. Gradient-based methods are the most popular  approaches used for solving the problem, owing to their simplicity and computational efficiency. These methods, however, do not achieve the information-theoretically optimal query complexity for minimizing the underlying function to small error, which are achieved by more expensive techniques based on cutting-plane methods. Is it possible to achieve the information-theoretically query complexity without using these more complex and computationally expensive methods? In this work, we use memory as a lens to understand this, and show that is is not possible to achieve optimal query complexity without using significantly more memory than that used by gradient descent.","doi":"10.24963/ijcai.2023/722","url":"https://ijcai.org/proceedings/2023/722","pdf":"https://ijcai.org/proceedings/2023/0722.pdf","markdown":"https://ijcai.org/proceedings/2023/722.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/722","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Sister Conferences Best Papers","track":"Sister Conferences Best Papers","number":722,"pages":{"first":6468,"last":6473},"keywords":["Sister Conferences Best Papers: Machine Learning"],"videos":[],"references":[{"position":1,"raw":"[Alon et al., 1999] Noga Alon, Yossi Matias, and Mario Szegedy. 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