  Due to its applications in many different places in machine learning and
other connected engineering applications, the problem of minimization of a
smooth function that satisfies the Polyak-{\L}ojasiewicz condition receives
much attention from researchers. Recently, for this problem, the authors of
recent work proposed an adaptive gradient-type method using an inexact
gradient. The adaptivity took place only with respect to the Lipschitz constant
of the gradient. In this paper, for problems with the Polyak-{\L}ojasiewicz
condition, we propose a full adaptive algorithm, which means that the
adaptivity takes place with respect to the Lipschitz constant of the gradient
and the level of the noise in the gradient. We provide a detailed analysis of
the convergence of the proposed algorithm and an estimation of the distance
from the starting point to the output point of the algorithm. Numerical
experiments and comparisons are presented to illustrate the advantages of the
proposed algorithm in some examples.
