@article{fournier:inria-00452791,...

@article{fournier:inria-00452791,

hal_id = {inria-00452791},

url = {http://hal.inria.fr/inria-00452791},

title = {{Lower Bounds for Comparison Based Evolution Strategies using VC-dimension and Sign Patterns}},

author = {Fournier, Herv{\'e} and Teytaud, Olivier},

abstract = {{We derive lower bounds on the convergence rate of 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 the shatter function lemma. In the special case of optimization of the sphere function, improved lower bounds are obtained by an argument based on the number of sign patterns.}},

keywords = {Evolutionary Algorithms;Parallel Optimization;Comparison-based algorithms;VC-dimension;Sign patterns;Complexity},

language = {Anglais},

affiliation = {Parall{\'e}lisme, R{\'e}seaux, Syst{\`e}mes d'information, Mod{\'e}lisation - PRISM , Laboratoire de Recherche en Informatique - LRI , TAO - INRIA Saclay - Ile de France},

publisher = {Springer},

journal = {Algorithmica},

audience = {internationale },

year = {2010},

pdf = {http://hal.inria.fr/inria-00452791/PDF/evolution.pdf},

}

@incollection{teytaud:inria-00593179,

hal_id = {inria-00593179},

url = {http://hal.inria.fr/inria-00593179},

title = {{Lower Bounds for Evolution Strategies}},

author = {Teytaud, Olivier},

abstract = {{The mathematical analysis of optimization algorithms involves upper and lower bounds; we here focus on the second case. Whereas other chap- ters will consider black box complexity, we will here consider complexity based on the key assumption that the only information available on the fitness values is the rank of individuals - we will not make use of the exact fitness values. Such a reduced information is known efficient in terms of ro- bustness (Gelly et al., 2007), what gives a solid theoretical foundation to the robustness of evolution strategies, which is often argued without mathemat- ical rigor - and we here show the implications of this reduced information on convergence rates. In particular, our bounds are proved without infi- nite dimension assumption, and they have been used since that time for designing algorithms with better performance in the parallel setting.}},

language = {Anglais},

affiliation = {Laboratoire de Recherche en Informatique - LRI , TAO - INRIA Saclay - Ile de France},

booktitle = {{Theory of Randomized Search Heuristics}},

publisher = {World Scientific},

pages = {327-354},

volume = {1},

editor = {Anne Auger, Benjamin Doerr },

series = {Series on Theoretical Computer Science },

audience = {internationale },

year = {2011},

month = May,

pdf = {http://hal.inria.fr/inria-00593179/PDF/ws-book9x6.pdf},

}

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