Algorithm Portfolios for Noisy Optimization

Noisy optimization is the optimization of objective functions corrupted by noise. A portfolio of solvers is a set of solvers equipped with an algorithm selection tool for distributing the computational power among them. Portfolios are widely and successfully used in combinatorial optimization. In this work, we study portfolios of noisy optimization solvers. We obtain mathematically proved performance (in the sense that the portfolio performs nearly as well as the best of its solvers) by an ad hoc portfolio algorithm dedicated to noisy optimization. A somehow surprising result is that it is better to compare solvers with some lag, i.e., propose the current recommendation of best solver based on their performance earlier in the run. An additional finding is a principled method for distributing the computational power among solvers in the portfolio.Comment: in Annals of Mathematics and Artificial Intelligence, Springer Verlag, 201

Contribution to the study of the fruits of Moroccan ferules

Une approche biométrique, morphologique et anatomique des fruits de 31 populations de férules marocaines rattachées à Ferula atlantica Elalaoui& Cauwet, F. communis L., F. cossoniana Batt. & Trabut, F. gouliminensis Elalaoui & Cauwet, F. sauvagei Elalaoui & Cauwet et F. tingitana L. à mis en évidence l’existence: -d’une variation importante de la taille du fruit, -d’une variation de la taille et du nombre de bandelettes, -d’un canal sécréteur uniquement au niveau des 3 côtes dorsales, -d’un tractus plus ou moins long dans l’aile des fruits étudiés sauf ceux de F. tingitana, -d’une couche de sire, plus ou moins développée, tapissant la surface du fruit au niveau commissural, -d’une singularité carpologique pour certains taxons: ainsi F. tingitana se distingue par des fruits longs et étroits à très peu de bandelettes à aile étroite sans tractus et à leptocarpe peu développé. A l’opposé F. cossoniana présente des fruits très arrondis à nombreuses bandelettes à aile large possédant un tractus et à leptocarpe formé d’une dizaine d’assises cellulaires. Pour ce dernier caractère F. cossoniana montre beaucoup de similitude avec F. gouliminensis.A biometric, morphological and anatomical approach of 31 populations of Moroccan ferules corresponding to Ferula atlantica Elalaoui & Cauwet, F. communis L., F. cossoniana Batt. & Trabut, F. gouliminensis Elalaoui & Cauwet, F. sauvagei Elalaoui & Cauwet and F. tingitana L. highlighted the following features: -significant variation of the fruit size, -variation of the size and the number of vittae, -an extra cannel only on the level of the 3 dorsal ridges, -more or less long tract at the fruits wing, except in F. tingitana, -more or less developed layer of wax at the commissural surface, -carpologic singularities for some taxa. Thus, F. tingitana is characterised by long and narrow fruits with very few vittae, with narrow wing without tract and leptocarpe with 3 to 5 cellular layers. On the contrary, F. cossoniana present very rounded fruits with many vittae, large wings having a tract and leptocarpe formed by 8 to 10 cellular layers. For this character, F. cossoniana shows strong similarity with F. gouliminensis

Depth, balancing, and limits of the Elo model

-Much work has been devoted to the computational complexity of games. However, they are not necessarily relevant for estimating the complexity in human terms. Therefore, human-centered measures have been proposed, e.g. the depth. This paper discusses the depth of various games, extends it to a continuous measure. We provide new depth results and present tool (given-first-move, pie rule, size extension) for increasing it. We also use these measures for analyzing games and opening moves in Y, NoGo, Killall Go, and the effect of pie rules

Geochemistry of the sahelian Gambia river during the 1983 high-water stage

La géochimie des rivières africaines est très peu connue comparativement à celle des fleuves des autres continents. Cette étude sur le cours moyen de la Gambie complète les récents travaux de Lesack et al. (1984-1985) dans la partie aval du fleuve et ceux de Gac et al. (1987) sur le haut bassin guinéen. Les flux dissous et de matières en suspension sont évalués à partir de la composition chimique moyenne (44 mg/l) et de la charge solide (47 mg/l). Le carbone organique particulaire représente de 1,2 à 8 % des matières en suspension. (Résumé d'auteur

Analysis of Different Types of Regret in Continuous Noisy Optimization

The performance measure of an algorithm is a crucial part of its analysis. The performance can be determined by the study on the convergence rate of the algorithm in question. It is necessary to study some (hopefully convergent) sequence that will measure how "good" is the approximated optimum compared to the real optimum. The concept of Regret is widely used in the bandit literature for assessing the performance of an algorithm. The same concept is also used in the framework of optimization algorithms, sometimes under other names or without a specific name. And the numerical evaluation of convergence rate of noisy algorithms often involves approximations of regrets. We discuss here two types of approximations of Simple Regret used in practice for the evaluation of algorithms for noisy optimization. We use specific algorithms of different nature and the noisy sphere function to show the following results. The approximation of Simple Regret, termed here Approximate Simple Regret, used in some optimization testbeds, fails to estimate the Simple Regret convergence rate. We also discuss a recent new approximation of Simple Regret, that we term Robust Simple Regret, and show its advantages and disadvantages.Comment: Genetic and Evolutionary Computation Conference 2016, Jul 2016, Denver, United States. 201

Noisy Optimization: Convergence with a Fixed Number of Resamplings

International audienceIt is known that evolution strategies in continuous domains might not converge in the presence of noise. It is also known that, under mild assumptions, and using an increasing number of resamplings, one can mitigate the effect of additive noise and recover convergence. We show new sufficient conditions for the convergence of an evolutionary algorithm with constant number of resamplings; in particular, we get fast rates (log-linear convergence) provided that the variance decreases around the optimum slightly faster than in the so-called multiplicative noise model

Multivariate bias reduction in capacity expansion planning

International audienceThe optimization of capacities in large scale power systems is a stochastic problem, because the need for storage and connections (i.e. exchange capacities) varies a lot from one week to another (e.g. power generation is subject to the vagaries of wind) and from one winter to another (e.g. water inflows due to snow melting). It is usually tackled through sample average approximation, i.e. assuming that the system which is optimal on average over the last 40 years (corrected for climate change) is also approximately optimal in general. However, in many cases, data are high-dimensional; the sample complexity, i.e. the amount of data necessary for a relevant optimization of capacities, increases linearly with the number of parameters and can be scarcely available at the relevant scale. This leads to an underestimation of capacities. We suggest the use of bias correction in capacity estimation. The present paper investigates the importance of the bias phenomenon, and the efficiency of bias correction tools (jackknife, bootstrap; combined with possibly penalized cross-validation) including new ones (dimension reduction tools, margin method

Fully Parallel Hyperparameter Search: Reshaped Space-Filling

Space-filling designs such as scrambled-Hammersley, Latin Hypercube Sampling and Jittered Sampling have been proposed for fully parallel hyperparameter search, and were shown to be more effective than random or grid search. In this paper, we show that these designs only improve over random search by a constant factor. In contrast, we introduce a new approach based on reshaping the search distribution, which leads to substantial gains over random search, both theoretically and empirically. We propose two flavors of reshaping. First, when the distribution of the optimum is some known $P_0$, we propose Recentering, which uses as search distribution a modified version of $P_0$ tightened closer to the center of the domain, in a dimension-dependent and budget-dependent manner. Second, we show that in a wide range of experiments with $P_0$ unknown, using a proposed Cauchy transformation, which simultaneously has a heavier tail (for unbounded hyperparameters) and is closer to the boundaries (for bounded hyperparameters), leads to improved performances. Besides artificial experiments and simple real world tests on clustering or Salmon mappings, we check our proposed methods on expensive artificial intelligence tasks such as attend/infer/repeat, video next frame segmentation forecasting and progressive generative adversarial networks