Black-box Optimizer with Implicit Natural Gradient

TL;DR

This paper introduces a new black-box optimization method using implicit natural gradients, offering theoretical convergence guarantees and competitive empirical performance with fewer hyperparameters than CMA-ES.

Contribution

It presents a novel implicit natural gradient framework for black-box optimization with proven convergence and improved efficiency over existing methods like IGO.

Findings

Achieves competitive results on benchmark problems.

Converges for convex and non-differentiable functions.

Requires fewer hyperparameters than CMA-ES.

Abstract

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.