  We present a canonical way to turn any smooth parametric family of
probability distributions on an arbitrary search space $X$ into a
continuous-time black-box optimization method on $X$, the
\emph{information-geometric optimization} (IGO) method. Invariance as a design
principle minimizes the number of arbitrary choices. The resulting \emph{IGO
flow} conducts the natural gradient ascent of an adaptive, time-dependent,
quantile-based transformation of the objective function. It makes no
assumptions on the objective function to be optimized.
  The IGO method produces explicit IGO algorithms through time discretization.
It naturally recovers versions of known algorithms and offers a systematic way
to derive new ones. The cross-entropy method is recovered in a particular case,
and can be extended into a smoothed, parametrization-independent maximum
likelihood update (IGO-ML). For Gaussian distributions on $\mathbb{R}^d$, IGO
is related to natural evolution strategies (NES) and recovers a version of the
CMA-ES algorithm. For Bernoulli distributions on $\{0,1\}^d$, we recover the
PBIL algorithm. From restricted Boltzmann machines, we obtain a novel algorithm
for optimization on $\{0,1\}^d$. All these algorithms are unified under a
single information-geometric optimization framework.
  Thanks to its intrinsic formulation, the IGO method achieves invariance under
reparametrization of the search space $X$, under a change of parameters of the
probability distributions, and under increasing transformations of the
objective function.
  Theory strongly suggests that IGO algorithms have minimal loss in diversity
during optimization, provided the initial diversity is high. First experiments
using restricted Boltzmann machines confirm this insight. Thus IGO seems to
provide, from information theory, an elegant way to spontaneously explore
several valleys of a fitness landscape in a single run.
