Handling Expensive Optimization with Large Noise

Rémi Coulom 1 Philippe Rolet 2, 3 Nataliya Sokolovska 2, 3 Olivier Teytaud 2, 3
1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
2 TAO - Machine Learning and Optimisation
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique
Abstract : This paper exhibits lower and upper bounds on runtimes for expensive noisy optimization problems. Runtimes are expressed in terms of number of fitness evaluations. Fitnesses considered are monotonic transformations of the {\em sphere} function. The analysis focuses on the common case of fitness functions quadratic in the distance to the optimum in the neighborhood of this optimum---it is nonetheless also valid for any monotonic polynomial of degree p>2. Upper bounds are derived via a bandit-based estimation of distribution algorithm that relies on Bernstein races called R-EDA. It is known that the algorithm is consistent even in non-differentiable cases. Here we show that: (i) if the variance of the noise decreases to 0 around the optimum, it can perform optimally for quadratic transformations of the norm to the optimum, (ii) otherwise, it provides a slower convergence rate than the one exhibited empirically by an algorithm called Quadratic Logistic Regression based on surrogate models---although QLR requires a probabilistic prior on the fitness class.
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Communication dans un congrès
ACM. Foundations of Genetic Algorithms, Jan 2011, Austria. pp.TBA, 2011
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Rémi Coulom, Philippe Rolet, Nataliya Sokolovska, Olivier Teytaud. Handling Expensive Optimization with Large Noise. ACM. Foundations of Genetic Algorithms, Jan 2011, Austria. pp.TBA, 2011. 〈hal-00517157v2〉

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