Minimisation of Polyak-Łojasewicz Functions Using Random Zeroth-Order Oracles
This work addresses optimization challenges in scenarios where gradient information is unavailable, offering a method for zeroth-order optimization with theoretical guarantees, though it appears incremental as it builds on existing PL function frameworks.
The paper tackles the problem of minimizing Polyak-Łojasewicz functions using a zeroth-order scheme with a random oracle for gradient estimation, achieving convergence to a global minimum in unconstrained cases and to a neighborhood in constrained cases with provided complexity bounds.
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.