  We consider the problem of optimizing a robot morphology to achieve the best
performance for a target task, under computational resource limitations. The
evaluation process for each morphological design involves learning a controller
for the design, which can consume substantial time and computational resources.
To address the challenge of expensive robot morphology evaluation, we present a
continuous multi-fidelity Bayesian Optimization framework that efficiently
utilizes computational resources via low-fidelity evaluations. We identify the
problem of non-stationarity over fidelity space. Our proposed fidelity warping
mechanism can learn representations of learning epochs and tasks to model
non-stationary covariances between continuous fidelity evaluations which prove
challenging for off-the-shelf stationary kernels. Various experiments
demonstrate that our method can utilize the low-fidelity evaluations to
efficiently search for the optimal robot morphology, outperforming
state-of-the-art methods.
