Adversarial attacks based on randomized search schemes have obtained state-of-the-art results in black-box robustness evaluation recently. However, as we demonstrate in this work, their efficiency in different query budget regimes depends on manual design and heuristic tuning of the underlying proposal distributions. We study how this issue can be addressed by adapting the proposal distribution online based on the information obtained during the attack. We consider Square Attack, which is a state-of-the-art score-based black-box attack, and demonstrate how its performance can be improved by a learned controller that adjusts the parameters of the proposal distribution online during the attack. We train the controller using gradient-based end-to-end training on a CIFAR10 model with white box access.