Abstract

We are interested in the optimization of a high-dimensional function when only function evaluations are possible. Although this derivative-free setting arises in many applications, existing methods suffer from high sample complexity since their sample complexity depend on problem dimensionality, in contrast to the dimensionality-independent rates of first-order methods. The recent success of deep learning methods suggests that many data modalities lie on low-dimensional manifolds that can be represented by deep nonlinear models. Based on this observation, we consider derivative-free optimization of functions defined on lowdimensional manifolds. 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 proposed method significantly reduces sample complexity. We empirically evaluate the presented method on continuous optimization benchmarks and high-dimensional continuous control problems. Our method achieves significantly lower sample complexity than Augmented Random Search and other derivative-free optimization algorithms.