A. Conn, K. Scheinberg, and L. Toint, Recent progress in unconstrained nonlinear optimization without derivatives, Mathematical Programming, vol.12, issue.1, 1997.
DOI : 10.1007/BF02614326

B. Doerr and C. Winzen, Towards a Complexity Theory of Randomized Search Heuristics: Ranking-Based Black-Box Complexity, CSR, ser. Lecture Notes in Computer Science, pp.15-28, 2011.
DOI : 10.1017/CBO9780511814075

S. Grünewälder, J. Audibert, M. Opper, and J. Shawe-taylor, Regret Bounds for Gaussian Process Bandit Problems, Conference Proceedings : AISTATS 2010, pp.273-280, 2010.

H. Schwefel, Numerical Optimization of Computer Models, pp.1995-1997, 1981.

H. Beyer, Mutate large, but inherit small ! On the analysis of mutations in (1, ?)-ES with noisy fitness data, Proc. of the 5 th Conference on Parallel Problems Solving from Nature, pp.109-118, 1998.

J. Fitzpatrick and J. Grefenstette, Genetic algorithms in noisy environments, in machine learning: Special issue on genetic algorithms, 1988.

D. V. Arnold and H. Beyer, Local performance of the (1 + 1)-ES in a noisy environment, IEEE Transactions on Evolutionary Computation, vol.6, issue.1, pp.30-41, 2002.
DOI : 10.1109/4235.985690

D. V. Arnold and H. Beyer, Evolution strategies with cumulative step length adaptation on the noisy parabolic ridge, Natural Computing, vol.2, issue.2, 2006.
DOI : 10.1007/s11047-006-9025-5

U. Hammel and T. Bäck, Evolution strategies on noisy functions: How to improve convergence properties, " in Parallel Problem Solving From Nature, pp.9-14, 1994.

J. M. Fitzpatrick and J. J. Grefenstette, Genetic algorithms in noisy environments, Machine Learning, pp.101-120, 1988.
DOI : 10.1007/BF00113893

M. Jebalia and A. Auger, On Multiplicative Noise Models for Stochastic Search, Parallel Problem Solving From Nature, 2008.
DOI : 10.1007/978-3-540-87700-4_6

URL : https://hal.archives-ouvertes.fr/inria-00287725

O. Teytaud and A. Auger, On the adaptation of noise level for stochastic optimization, 2007 IEEE Congress on Evolutionary Computation, 2007.
DOI : 10.1109/CEC.2007.4424857

URL : https://hal.archives-ouvertes.fr/inria-00173224

R. Coulom, CLOP: Confident Local Optimization for Noisy??Black-Box Parameter Tuning, Lecture Notes in Computer Science, H. J. van den, vol.7168, pp.146-157, 2011.
DOI : 10.1007/978-3-642-31866-5_13

URL : https://hal.archives-ouvertes.fr/hal-00750326

R. Coulom, P. Rolet, N. Sokolovska, and O. Teytaud, Handling expensive optimization with large noise, Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms, FOGA '11, pp.61-68, 2011.
DOI : 10.1145/1967654.1967660

URL : https://hal.archives-ouvertes.fr/hal-00517157

P. Rolet and O. Teytaud, Bandit-Based Estimation of Distribution Algorithms for Noisy Optimization: Rigorous Runtime Analysis, Proceedings of Lion4 (accepted), 2009.
DOI : 10.1007/978-3-642-13800-3_8

URL : https://hal.archives-ouvertes.fr/inria-00437140

V. Heidrich-meisner and C. Igel, Uncertainty handling CMA-ES for reinforcement learning, Proceedings of the 11th Annual conference on Genetic and evolutionary computation, GECCO '09, pp.1211-1218, 2009.
DOI : 10.1145/1569901.1570064

L. Devroye, L. Györfi, and G. Lugosi, A probabilistic Theory of Pattern Recognition, 1997.
DOI : 10.1007/978-1-4612-0711-5

R. Coulom, P. Rolet, N. Sokolovska, and O. Teytaud, Handling expensive optimization with large noise, Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms, FOGA '11, pp.61-68, 2011.
DOI : 10.1145/1967654.1967660

URL : https://hal.archives-ouvertes.fr/hal-00517157

D. R. Jones, M. Schonlau, and W. J. Welch, Efficient global optimization of expensive black-box functions, Journal of Global Optimization, vol.13, issue.4, pp.455-492, 1998.
DOI : 10.1023/A:1008306431147

J. Villemonteix, E. Vazquez, and E. Walter, An informational approach to the global optimization of expensive-to-evaluate functions, Journal of Global Optimization, vol.10, issue.5, p.26, 2008.
DOI : 10.1007/s10898-008-9354-2

URL : https://hal.archives-ouvertes.fr/hal-00354262

V. Fabian, Stochastic Approximation of Minima with Improved Asymptotic Speed, The Annals of Mathematical Statistics, vol.38, issue.1, pp.191-200, 1967.
DOI : 10.1214/aoms/1177699070

L. Bienaymé, ConsidérationsConsidérations`Considérationsà l'appui de la découverte de laplace, Comptes Rendus de l'Académie des Sciences, pp.309-324, 1853.

P. Chebyshev, Sur les valeurs limites des integrales, Math Pure Appl, vol.19, pp.157-160

A. Markov, On certain applications of algebraic continued fractions, 2002.

O. Teytaud and S. Gelly, General Lower Bounds for Evolutionary Algorithms, 10 th International Conference on Parallel Problem Solving from Nature, 2006.
DOI : 10.1007/11844297_3

URL : https://hal.archives-ouvertes.fr/inria-00112820

H. Fournier and O. Teytaud, Lower Bounds for Comparison Based Evolution Strategies Using VC-dimension and Sign Patterns, Algorithmica, vol.XVI, issue.2, pp.387-408, 2011.
DOI : 10.1007/s00453-010-9391-3

URL : https://hal.archives-ouvertes.fr/inria-00452791

A. Auger, Convergence results for the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>??</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-SA-ES using the theory of <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>??</mml:mi></mml:math>-irreducible Markov chains, Theoretical Computer Science, vol.334, issue.1-3, pp.35-69, 2005.
DOI : 10.1016/j.tcs.2004.11.017

A. Auger, M. Schoenauer, and O. Teytaud, Local and global order 3/2 convergence of a surrogate evolutionnary algorithm, Gecco, p.8, 2005.

D. V. Arnold and H. Beyer, Efficiency and mutation strength adaptation of the (mu/mui,lambda)-es in a noisy environment, Parallel Problem Solving from Nature, pp.39-48, 1917.

H. Beyer, The Theory of Evolution Strategies, ser. Natural Computing Series, 2001.

H. Chen, Lower Rate of Convergence for Locating a Maximum of a Function, The Annals of Statistics, vol.16, issue.3, pp.1330-1334, 1988.
DOI : 10.1214/aos/1176350965

J. Kiefer and J. Wolfowitz, Stochastic Estimation of the Maximum of a Regression Function, The Annals of Mathematical Statistics, vol.23, issue.3, pp.462-466, 1952.
DOI : 10.1214/aoms/1177729392

E. Vazquez, J. Villemonteix, M. Sidorkiewicz, and E. Walter, Global optimization based on noisy evaluations: An empirical study of two statistical approaches, Journal of Physics: Conference Series, vol.135, p.17, 2008.
DOI : 10.1088/1742-6596/135/1/012100

URL : https://hal.archives-ouvertes.fr/hal-00278188