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Bibliographic Details
Main Authors: Cha, Jinho, Kim, Youngchul, Shin, Jungmin, Cho, Jaeyoung, Kim, Seon Jin, Ryu, Junyeol
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2510.20227
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Table of 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.