Objective improvement in information-geometric optimization
Youhei Akimoto, Yann Ollivier · 2013
Information-Geometric Optimization (IGO) is a unified framework of stochastic algorithms for optimization problems. Given a family of probability distributions, IGO turns the original optimization problem into a new maximization problem on the parameter space of the probability distributions. IGO updates the parameter of the probability distribution along the natural gradient, taken with respect to the Fisher metric on the parameter manifold, aiming at maximizing an adaptive transform of the objective function. IGO recovers several known algorithms as particular instances: for the family of Bernoulli distributions IGO recovers PBIL, for the family of Gaussian distributions the pure rank-μ CMA-ES update is recovered, and for exponential families in expectation parametrization the cross-entropy/ML method is recovered.