Minimisation of Polyak-Łojasewicz Functions Using Random Zeroth-Order Oracles

Amir Ali Farzin, Iman Shames
5/15/2024
math.OCcs.LG

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Abstract

The application of a zeroth-order scheme for minimising Polyak-Łojasewicz (PL) functions is considered. The framework is based on exploiting a random oracle to estimate the function gradient. The convergence of the algorithm to a global minimum in the unconstrained case and to a neighbourhood of the global minimum in the constrained case along with their corresponding complexity bounds are presented. The theoretical results are demonstrated via numerical examples.

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Cite this paper

@article{farzin2024minimisation,
  title  = {Minimisation of Polyak-Łojasewicz Functions Using Random Zeroth-Order Oracles},
  author = {Amir Ali Farzin and Iman Shames},
  year   = {2024},
  eprint = {2405.09106},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2405.09106v1}
}

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