Corpus ID: 201310409

A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization

@article{Xie2019AGA,
  title={A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization},
  author={Guangzeng Xie and Luo Luo and Zhihua Zhang},
  journal={ArXiv},
  year={2019},
  volume={abs/1908.08394}
}

Guangzeng Xie, Luo Luo, Zhihua Zhang

Published 2019

Mathematics, Computer Science

ArXiv

This paper studies the lower bound complexity for the optimization problem whose objective function is the average of $n$ individual smooth convex functions. We consider the algorithm which gets access to gradient and proximal oracle for each individual component. For the strongly-convex case, we prove such an algorithm can not reach an $\varepsilon$-suboptimal point in fewer than $\Omega((n+\sqrt{\kappa n})\log(1/\varepsilon))$ iterations, where $\kappa$ is the condition number of the… CONTINUE READING

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