  We are interested in derivative-free optimization of high-dimensional
functions. The sample complexity of existing methods is high and depends on
problem dimensionality, unlike the dimensionality-independent rates of
first-order methods. The recent success of deep learning suggests that many
datasets lie on low-dimensional manifolds that can be represented by deep
nonlinear models. We therefore consider derivative-free optimization of a
high-dimensional function that lies on a latent low-dimensional manifold. We
develop an online learning approach that learns this manifold while performing
the optimization. In other words, we jointly learn the manifold and optimize
the function. Our analysis suggests that the presented method significantly
reduces sample complexity. We empirically evaluate the method on continuous
optimization benchmarks and high-dimensional continuous control problems. Our
method achieves significantly lower sample complexity than Augmented Random
Search, Bayesian optimization, covariance matrix adaptation (CMA-ES), and other
derivative-free optimization algorithms.
