Corpus ID: 201310409

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

  title={A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization},
  author={Guangzeng Xie and Luo Luo and Zhihua Zhang},
  • 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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