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This paper explores the use of the standard approach for proving runtimebounds in discrete domains---often referred to as drift analysis---in thecontext of optimization on a continuous domain. Using this framework we analyzethe (1+1) Evolution Strategy with one-fifth success rule on the spherefunction. To deal with potential functions that are not lower-bounded, weformulate novel drift theorems. We then use the theorems to prove bounds on theexpected hitting time to reach a certain target fitness in finite dimension$d$. The bounds are akin to linear convergence. We then study the dependency ofthe different terms on $d$ proving a convergence rate dependency of$\Theta(1/d)$. Our results constitute the first non-asymptotic analysis for thealgorithm considered as well as the first explicit application of driftanalysis to a randomized search heuristic with continuous domain.

Drift Theory in Continuous Search Spaces: Expected Hitting Time of the (1+1)-ES with 1/5 Success Rule