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We consider channel estimation in systems equipped with a reconfigurable intelligent surface (RIS). In order to illuminate the additional cascaded channel as compared to systems without a RIS, commonly an unaffordable amount of pilot sequences has to be transmitted over different phase allocations at the RIS. However, for a given base station (BS) cell, there exist immanent structural characteristics of the environment which can be leveraged to reduce the necessary number of phase allocations. We verify this observation by a study on discrete Fourier transform (DFT)-based phase allocations where we exhaustively search for the best combination of DFT columns. Since this brute-force search is unaffordable in practice, we propose to learn a neural network (NN) for joint phase optimization and channel estimation because of the dependency of the optimal phase allocations on the channel estimator, and vice versa. We verify the effectiveness of the approach by numerical simulations where common choices for the phase allocations and the channel estimator are outperformed. By an ablation study, the learned phase allocations are shown to be beneficial in combination with a different state-of-the-art channel estimator as well.