{"date_updated":"2024-04-29T07:05:41Z","main_file_link":[{"open_access":"1","url":"https://proceedings.mlr.press/v130/alimisis21a.html"}],"alternative_title":["PMLR"],"conference":{"end_date":"2021-04-15","location":"San Diego, CA, United States; Virtual","name":"AISTATS: Conference on Artificial Intelligence and Statistics","start_date":"2021-04-13"},"acknowledgement":"The authors would like to thank professors Nicolas Boumal and Suvrit Sra for helpful discussions on the content of this paper. Gary Bécigneul was funded by the Max Planck ETH Center for Learning Systems during the course of this work.","title":"Momentum improves optimization on Riemannian manifolds","intvolume":"       130","type":"conference","citation":{"chicago":"Alimisis, Foivos, Antonio Orvieto, Gary Becigneul, and Aurelien Lucchi. “Momentum Improves Optimization on Riemannian Manifolds.” In <i>Proceedings of the 24th International Conference on Artificial Intelligence and Statistics</i>, 130:1351–59. ML Research Press, 2021.","short":"F. Alimisis, A. Orvieto, G. Becigneul, A. Lucchi, in:, Proceedings of the 24th International Conference on Artificial Intelligence and Statistics, ML Research Press, 2021, pp. 1351–1359.","ista":"Alimisis F, Orvieto A, Becigneul G, Lucchi A. 2021. Momentum improves optimization on Riemannian manifolds. Proceedings of the 24th International Conference on Artificial Intelligence and Statistics. AISTATS: Conference on Artificial Intelligence and Statistics, PMLR, vol. 130, 1351–1359.","mla":"Alimisis, Foivos, et al. “Momentum Improves Optimization on Riemannian Manifolds.” <i>Proceedings of the 24th International Conference on Artificial Intelligence and Statistics</i>, vol. 130, ML Research Press, 2021, pp. 1351–59.","ieee":"F. Alimisis, A. Orvieto, G. Becigneul, and A. Lucchi, “Momentum improves optimization on Riemannian manifolds,” in <i>Proceedings of the 24th International Conference on Artificial Intelligence and Statistics</i>, San Diego, CA, United States; Virtual, 2021, vol. 130, pp. 1351–1359.","apa":"Alimisis, F., Orvieto, A., Becigneul, G., &#38; Lucchi, A. (2021). Momentum improves optimization on Riemannian manifolds. In <i>Proceedings of the 24th International Conference on Artificial Intelligence and Statistics</i> (Vol. 130, pp. 1351–1359). San Diego, CA, United States; Virtual: ML Research Press.","ama":"Alimisis F, Orvieto A, Becigneul G, Lucchi A. Momentum improves optimization on Riemannian manifolds. In: <i>Proceedings of the 24th International Conference on Artificial Intelligence and Statistics</i>. Vol 130. ML Research Press; 2021:1351-1359."},"quality_controlled":"1","abstract":[{"text":"We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to hold for geodesically strongly-convex objective functions. We further extend our algorithm to geodesically weakly-quasi-convex objectives. Our proofs of convergence rely on a novel estimate sequence that illustrates the dependency of the convergence rate on the curvature of the manifold. We validate our theoretical results empirically on several optimization problems defined on the sphere and on the manifold of positive definite matrices.","lang":"eng"}],"year":"2021","department":[{"_id":"DaAl"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":130,"oa":1,"publication":"Proceedings of the 24th International Conference on Artificial Intelligence and Statistics","_id":"15263","day":"15","status":"public","date_created":"2024-04-03T07:29:49Z","language":[{"iso":"eng"}],"external_id":{"arxiv":["2002.04144"]},"page":"1351-1359","author":[{"last_name":"Alimisis","first_name":"Foivos","id":"19430a34-05f6-11ef-890d-c079cfc60ae2","full_name":"Alimisis, Foivos"},{"last_name":"Orvieto","first_name":"Antonio","full_name":"Orvieto, Antonio"},{"full_name":"Becigneul, Gary","first_name":"Gary","last_name":"Becigneul"},{"first_name":"Aurelien","full_name":"Lucchi, Aurelien","last_name":"Lucchi"}],"publisher":"ML Research Press","oa_version":"Published Version","month":"04","article_processing_charge":"No","date_published":"2021-04-15T00:00:00Z","publication_status":"published"}