Learning-to-Learn to Guide Random Search: Derivative-Free Meta Blackbox Optimization on Manifold

Solving a sequence of high-dimensional, nonconvex, but potentially similar optimization problems poses a computational challenge in engineering applications. We propose the first meta-learning framework that leverages the shared structure among sequential tasks to improve the computational efficiency and sample complexity of derivative-free optimization. Based on the observation that most practical high-dimensional functions lie on a latent low-dimensional manifold, which can be further shared among instances, our method jointly learns the meta-initialization of a search point and a meta-manifold. Theoretically, we establish the benefit of meta-learning in this challenging setting. Empirically, we demonstrate the effectiveness of the proposed algorithm in two high-dimensional reinforcement learning tasks.