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Minimisation of Polyak-Łojasewicz Functions Using Random Zeroth-Order Oracles (2405.09106v1)
Published 15 May 2024 in math.OC and cs.LG
Abstract: 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.