June 10, 2024, 4:46 a.m. | Ioannis Mavrothalassitis, Stratis Skoulakis, Leello Tadesse Dadi, Volkan Cevher

cs.LG updates on arXiv.org arxiv.org

arXiv:2406.04731v1 Announce Type: cross
Abstract: Given a sequence of functions $f_1,\ldots,f_n$ with $f_i:\mathcal{D}\mapsto \mathbb{R}$, finite-sum minimization seeks a point ${x}^\star \in \mathcal{D}$ minimizing $\sum_{j=1}^n f_j(x)/n$. In this work, we propose a key twist into the finite-sum minimization, dubbed as continual finite-sum minimization, that asks for a sequence of points ${x}_1^\star,\ldots,{x}_n^\star \in \mathcal{D}$ such that each ${x}^\star_i \in \mathcal{D}$ minimizes the prefix-sum $\sum_{j=1}^if_j(x)/i$. Assuming that each prefix-sum is strongly convex, we develop a first-order continual stochastic variance reduction gradient method ($\mathrm{CSVRG}$) …

abstract arxiv continual cs.lg functions key math.oc star sum type work

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