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Most current approaches to undersampled multi-coil MRI reconstruction focus on learning the reconstruction model for a fixed, equidistant acquisition trajectory. In this paper, we study the problem of joint learning of the reconstruction model together with acquisition policies. To this end, we extend the End-to-End Variational Network with learnable acquisition policies that can adapt to different data points. We validate our model on a coil-compressed version of the large scale undersampled multi-coil fastMRI dataset using two undersampling factors: $4\times$ and $8\times$. Our experiments show on-par performance with the learnable non-adaptive and handcrafted equidistant strategies at $4\times$, and an observed improvement of more than $2\%$ in SSIM at $8\times$ acceleration, suggesting that potentially-adaptive $k$-space acquisition trajectories can improve reconstructed image quality for larger acceleration factors. However, and perhaps surprisingly, our best performing policies learn to be explicitly non-adaptive.