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Due to its applications in many different places in machine learning andother connected engineering applications, the problem of minimization of asmooth function that satisfies the Polyak-{\L}ojasiewicz condition receivesmuch attention from researchers. Recently, for this problem, the authors ofrecent work proposed an adaptive gradient-type method using an inexactgradient. The adaptivity took place only with respect to the Lipschitz constantof the gradient. In this paper, for problems with the Polyak-{\L}ojasiewiczcondition, we propose a full adaptive algorithm, which means that theadaptivity takes place with respect to the Lipschitz constant of the gradientand the level of the noise in the gradient. We provide a detailed analysis ofthe convergence of the proposed algorithm and an estimation of the distancefrom the starting point to the output point of the algorithm. Numericalexperiments and comparisons are presented to illustrate the advantages of theproposed algorithm in some examples.

Gradient-Type Methods for Optimization Problems with Polyak-{\L}ojasiewicz Condition: Early Stopping and Adaptivity to Inexactness Parameter