We present a novel end-to-end deep learning-based adaptation control algorithm for frequency-domain adaptive system identification. The proposed method exploits a deep neural network to map observed signal features to corresponding step-sizes which control the filter adaptation. The parameters of the network are optimized in an end-to-end fashion by minimizing the average normalized system distance of the adaptive filter. This avoids the need of explicit signal power spectral density estimation as required for model-based adaptation control and further auxiliary mechanisms to deal with model inaccuracies. The proposed algorithm achieves fast convergence and robust steady-state performance for scenarios characterized by high-level, non-white and non-stationary additive noise signals, abrupt environment changes and additional model inaccuracies.