Robust estimation of natural gradient in optimization by regularized linear regression

Abstract

We are interested in the optimization of the expected value of a function by following a steepest descent policy over a statistical model. Such approach appears in many different model-based search meta-heuristics for optimization, for instance in the large class of random search methods in stochastic optimization and Evolutionary Computation. We study the case when statistical models belong to the exponential family and the direction of maximum decrement of the expected value is given by the natural gradient evaluated with respect to the Fisher Information metric. When the gradient cannot be computed exactly, a robust estimation allows to minimize the number of function evaluations required to obtain convergence to the global optimum. Under the choice of centered sufficient statistics, the estimation of the natural gradient corresponds to solving a least squares regression problem for the original function to be optimized. The correspondence between the estimation of the natural gradient and solving a linear regression problem leads to the definition of regularized versions of the natural gradient. We propose a robust estimation of the natural gradient for the exponential family based on regularized least squares. © 2013 Springer-Verlag.