A Stochastic Derivative-Free Optimization Method with Importance \n Sampling

Abstract

We consider the problem of unconstrained minimization of a smooth objectivefunction in $\mathbb{R}^n$ in a setting where only function evaluations arepossible. While importance sampling is one of the most popular techniques usedby machine learning practitioners to accelerate the convergence of their modelswhen applicable, there is not much existing theory for this acceleration in thederivative-free setting. In this paper, we propose an importance samplingversion of the stochastic three points ($\texttt{STP}$) method proposed byBergou et al. and derive new improved complexity results on non-convex, convexand $\lambda$-strongly convex functions. We conduct extensive experiments onvarious synthetic and real LIBSVM datasets confirming our theoretical results.We further test our method on a collection of continuous control tasks onseveral MuJoCo environments with varying difficulty. Our results suggest that$\texttt{STP}$ is practical for high dimensional continuous control problems.Moreover, the proposed importance sampling version results in a significantsample complexity improvement.