**Wednesday, 16:15 - 16:40 h, Room: H 3503**

**Anne Auger**

Convergence of adaptive evolution strategies on monotonic *C*^{2}-composite and scale-invariant functions

**Coauthors: Youhei Akimoto, Nikolaus Hansen**

**Abstract:**

Evolution Strategies (ES) are stochastic search algorithms for numerical black-box optimization where a family of probability distributions is iteratively adapted to ultimately converge to a distribution concentrated on optima of the function. They are derivative-free methods using the objective function through the ranking of candidate solutions. Hence they are invariant when optimizing *f* or *g º f* where *g:***R** → **R** is monotonically increasing. Recently, some adaptive ESs where shown to be stochastic approximations of a natural gradient algorithm in the manifold defined by the family of probability distributions. An ODE is naturally associated to this natural gradient algorithm when the step-size goes to zero. Solutions of this ODE are continuous time models of the underlying algorithms.

In this talk we will present convergence results of the solutions of this ODE and prove their local convergence on monotonic *C*^{2}-composite functions towards local optima of the function. We will also present global convergence of the corresponding algorithm on some scale-invariant functions defined as functions such that *f(x) < f(y)* iff *f(s x) < f(s y)* for all *s > 0*.

Talk 3 of the contributed session Wed.3.H 3503

**"Stochastic zero-order methods"** [...]

Cluster 6

**"Derivative-free & simulation-based optimization"** [...]