Blind Estimation of Audio Effects (BE-AFX) aims at estimating the audio effects (AFXs) applied to an original, unprocessed audio sample solely based on the processed audio sample. To train such a system traditional approaches optimize a loss between ground truth and estimated AFX parameters. This involves knowing the exact implementation of the AFXs used for the process. In this work, we propose an alternative solution that eliminates the requirement for knowing this implementation. Instead, we introduce an auto-encoder approach, which optimizes an audio quality metric. We explore, suggest, and compare various implementations of commonly used mastering AFXs, using differential signal processing or neural approximations. Our findings demonstrate that our auto-encoder approach yields superior estimates of the audio quality produced by a chain of AFXs, compared to the traditional parameter-based approach, even if the latter provides a more accurate parameter estimation.