  We present $\mathcal{L}_1$-$\mathcal{GP}$, an architecture based on
$\mathcal{L}_1$ adaptive control and Gaussian Process Regression (GPR) for safe
simultaneous control and learning. On one hand, the $\mathcal{L}_1$ adaptive
control provides stability and transient performance guarantees, which allows
for GPR to efficiently and safely learn the uncertain dynamics. On the other
hand, the learned dynamics can be conveniently incorporated into the
$\mathcal{L}_1$ control architecture without sacrificing robustness and
tracking performance. Subsequently, the learned dynamics can lead to less
conservative designs for performance/robustness tradeoff. We illustrate the
efficacy of the proposed architecture via numerical simulations.
