{"type":"ScholarlyArticle","title":"Accelerated Multiplicative Weights Update Avoids Saddle Points Almost Always","authors":[{"name":"Yi Feng","slug":"yi-feng","given":"Yi","family":"Feng","affiliation":"Shanghai University of Finance and Economics"},{"name":"Ioannis Panageas","slug":"ioannis-panageas","given":"Ioannis","family":"Panageas","affiliation":"University of California , Irvine"},{"name":"Xiao Wang","slug":"xiao-wang","given":"Xiao","family":"Wang","affiliation":"Shanghai University of Finance and Economics"}],"abstract":"We consider nonconvex optimization problem with constraint that is a product of simplices. A commonly used algorithm in solving this type of problem is the Multiplicative Weights Update (MWU), an algorithm that is widely used in game theory, machine learning and multi agent systems. Despite it has been known that MWU avoids saddle points, there is a question that remains unaddressed:  ``Is there an accelerated version of MWU that avoids saddle points provably?'' In this paper we provide a positive answer to above question. We provide an accelerated MWU based on Riemannian Accelerated Gradient Descent, and prove that the Riemannian Accelerated Gradient Descent, thus the accelerated MWU, avoid saddle points.","doi":"10.24963/ijcai.2022/252","url":"https://ijcai.org/proceedings/2022/252","pdf":"https://ijcai.org/proceedings/2022/0252.pdf","markdown":"https://ijcai.org/proceedings/2022/252.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/252","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Constraint Satisfaction and Optimization","track":"Main Track","number":252,"pages":{"first":1811,"last":1817},"keywords":["Constraint Satisfaction and Optimization: Constraint Optimization","Agent-based and Multi-agent Systems: Multi-agent Learning"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986750","length_sec":81,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38984893","length_sec":271,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Arora et al., 2012] Sanjeev Arora, lEad Hazan, and Satyen Kale. 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