Bregman Lagrangian
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The Bregman–Lagrangian framework permits a systematic understanding of the matching rates associated with higher-order gradient methods in discrete and continuous time.[1] Based on Bregman divergence, the Lagrangian is a continuous time dynamical system whose Euler-Lagrange equations can be linked to Nesterov's accelerated gradient method for gradient-based optimization.[2] The associated Bregman Hamiltonian allows for practical implementation of numerical discretizations.[3]
References
- ↑ Wibisono, Andre; Wilson, Ashia C.; Jordan, Michael I. (March 14, 2016). "A variational perspective on accelerated methods in optimization". Proceedings of the National Academy of Sciences. 113 (47): E7351–E7358. arXiv:1603.04245v1. Bibcode:2016PNAS..113E7351W. doi:10.1073/pnas.1614734113. PMC 5127379. PMID 27834219.
- ↑ Zhang, Peiyuan; Orvieto, Antonio; Daneshmand, Hadi (2021). Rethinking the Variational Interpretation of Accelerated Optimization Methods. Curran Associates, Inc. pp. 14396–14406. Retrieved 17 December 2024. Search this book on
- ↑ Bravetti, Alessandro; Daza-Torres, Maria L.; Flores-Arguedas, Hugo; Betancourt, Michael (June 2023). "Bregman dynamics, contact transformations and convex optimization". Information Geometry. 6 (1): 355–377. doi:10.1007/s41884-023-00105-0.
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