Bregman Lagrangian
From HandWiki
Short description: Optimization method in numerical analysis
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] The approach has been generalized to optimization on Riemannian manifolds.[4]
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. doi:10.1073/pnas.1614734113. PMID 27834219. Bibcode: 2016PNAS..113E7351W.
- ↑ Zhang, Peiyuan; Orvieto, Antonio; Daneshmand, Hadi (2021). Rethinking the Variational Interpretation of Accelerated Optimization Methods. Curran Associates, Inc.. pp. 14396–14406. https://proceedings.neurips.cc/paper_files/paper/2021/hash/788d986905533aba051261497ecffcbb-Abstract.html. Retrieved 17 December 2024.
- ↑ 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.
- ↑ Duruisseaux, Valentin; Leok, Melvin (June 2022). "A Variational Formulation of Accelerated Optimization on Riemannian Manifolds". SIAM Journal on Mathematics of Data Science 4 (2): 649–674. doi:10.1137/21M1395648.
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