Black-box Optimizer with Implicit Natural Gradient
It addresses optimization for compute-intensive applications like reinforcement learning and robot control, offering a simpler, hyperparameter-efficient approach with theoretical guarantees, though it appears incremental relative to existing methods like CMA-ES and IGO.
The paper tackles black-box optimization by proposing a method using implicit natural gradient with an exponential-family distribution, achieving competitive performance against CMA-ES on benchmark problems and high precision on challenging functions like the l1-norm ellipsoid and Levy test problems.
Black-box optimization is primarily important for many compute-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 update with the implicit natural gradient of an exponential-family distribution. Theoretically, we prove the convergence rate of our framework with full matrix update for convex functions. Our theoretical results also hold for continuous non-differentiable black-box functions. Our methods are very simple and contain less hyper-parameters than CMA-ES \cite{hansen2006cma}. Empirically, our method with full matrix update achieves competitive performance compared with one of the state-of-the-art method CMA-ES on benchmark test problems. Moreover, our methods can achieve high optimization precision on some challenging test functions (e.g., $l_1$-norm ellipsoid test problem and Levy test problem), while methods with explicit natural gradient, i.e., IGO \cite{ollivier2017information} with full matrix update can not. This shows the efficiency of our methods.