Asymptotic Dynamics of Alternating Minimization for Non-Convex Optimization
arxiv(2024)
摘要
This study investigates the asymptotic dynamics of alternating minimization
applied to optimize a bilinear non-convex function with normally distributed
covariates. We employ the replica method from statistical physics in a
multi-step approach to precisely trace the algorithm's evolution. Our findings
indicate that the dynamics can be described effectively by a two–dimensional
discrete stochastic process, where each step depends on all previous time
steps, revealing a memory dependency in the procedure. The theoretical
framework developed in this work is broadly applicable for the analysis of
various iterative algorithms, extending beyond the scope of alternating
minimization.
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