Black-Box Optimizer with Stochastic Implicit Natural Gradient

Abstract

Black-box optimization is primarily important for many computationally intensive applications, including reinforcement learning (RL), robot control, etc. This paper presents a novel theoretical framework for black-box optimization, in which our method performs stochastic updates with an implicit natural gradient of an exponential-family distribution. Theoretically, we prove the convergence rate of our framework with full matrix update for convex functions under Gaussian distribution. Our methods are very simple and contain fewer hyper-parameters than CMA-ES [ 12 ]. Empirically, our method with full matrix update achieves competitive performance compared with one of the state-of-the-art methods CMA-ES on benchmark test problems. Moreover, our methods can achieve high optimization precision on some challenging test functions (e.g., $l_1$ l 1 -norm ellipsoid test problem and Levy test problem), while methods with explicit natural gradient, i.e., IGO [ 21 ] with full matrix update can not. This shows the efficiency of our methods.