Lower Bounds for Evolution Strategies Using VC-Dimension
- Cite this paper as:
- Teytaud O., Fournier H. (2008) Lower Bounds for Evolution Strategies Using VC-Dimension. In: Rudolph G., Jansen T., Beume N., Lucas S., Poloni C. (eds) Parallel Problem Solving from Nature – PPSN X. PPSN 2008. Lecture Notes in Computer Science, vol 5199. Springer, Berlin, Heidelberg
We derive lower bounds for comparison-based or selection-based algorithms, improving existing results in the continuous setting, and extending them to non-trivial results in the discrete case. This is achieved by considering the VC-dimension of the level sets of the fitness functions; results are then obtained through the use of Sauer’s lemma. In the special case of optimization of the sphere function, improved lower bounds are obtained by bounding the possible number of sign conditions realized by some systems of equations.
KeywordsEvolution Strategies Convergence ratio VC-dimension Sign conditions
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