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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2510.20227 |
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| _version_ | 1866915571560349696 |
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| author | Cha, Jinho Kim, Youngchul Shin, Jungmin Cho, Jaeyoung Kim, Seon Jin Ryu, Junyeol |
| author_facet | Cha, Jinho Kim, Youngchul Shin, Jungmin Cho, Jaeyoung Kim, Seon Jin Ryu, Junyeol |
| contents | We develop a general optimization-theoretic framework for Bregman-Variational Learning Dynamics (BVLD), a new class of operator-based updates that unify Bayesian inference, mirror descent, and proximal learning under time-varying environments. Each update is formulated as a variational optimization problem combining a smooth convex loss f_t with a Bregman divergence D_psi. We prove that the induced operator is averaged, contractive, and exponentially stable in the Bregman geometry. Further, we establish Fejer monotonicity, drift-aware convergence, and continuous-time equivalence via an evolution variational inequality (EVI). Together, these results provide a rigorous analytical foundation for well-posed and stability-guaranteed operator dynamics in nonstationary optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20227 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimization of Bregman Variational Learning Dynamics Cha, Jinho Kim, Youngchul Shin, Jungmin Cho, Jaeyoung Kim, Seon Jin Ryu, Junyeol Optimization and Control We develop a general optimization-theoretic framework for Bregman-Variational Learning Dynamics (BVLD), a new class of operator-based updates that unify Bayesian inference, mirror descent, and proximal learning under time-varying environments. Each update is formulated as a variational optimization problem combining a smooth convex loss f_t with a Bregman divergence D_psi. We prove that the induced operator is averaged, contractive, and exponentially stable in the Bregman geometry. Further, we establish Fejer monotonicity, drift-aware convergence, and continuous-time equivalence via an evolution variational inequality (EVI). Together, these results provide a rigorous analytical foundation for well-posed and stability-guaranteed operator dynamics in nonstationary optimization. |
| title | Optimization of Bregman Variational Learning Dynamics |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.20227 |