Minimisation of Polyak-\Lojasewicz Functions Using Random Zeroth-Order Oracles
<|reference_start|>Minimisation of Polyak-\Lojasewicz Functions Using Random Zeroth-Order Oracles: The application of a zeroth-order scheme for minimising Polyak-\L{}ojasewicz (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.<|reference_end|>
@article{farzin2024minimisation,
    title={Minimisation of Polyak-\L{}ojasewicz Functions Using Random Zeroth-Order
  Oracles},
    author={Amir Ali Farzin, Iman Shames},
    journal={arXiv preprint arXiv:2405.09106},
    year={2024},
    doi={10.23919/ECC64448.2024.10590822},
    archivePrefix={arXiv},
    eprint={2405.09106},
    primaryClass={math.OC cs.LG}
}