Du jeu de Go au Havannah : variantes d'UCT et coups décisifs

National audienceLes algorithmes de type fouille d'arbre Monte-Carlo et UCT (upper confidence tree) ont révolutionné le jeu de Go par ordinateur depuis 2006/2007. Quelques applications, encore rares, ont montré la généralité de ces approches, en particulier quand l'espace d'actions est trop grand pour les autres techniques, et quand l'état est complètement observable. Dans ce papier, nous testons cette généralité, en expérimentant UCT dans un autre jeu, le Havannah. Ce jeu est connu spécialement difficile pour les ordinateurs. Nous montrons que cette approche donne de bons résultats tout comme pour le jeu de Go, même si on peut noter quelques différences et en particulier la notion de coup décisif, inexistante en Go

Why one must use reweighting in Estimation Of Distribution Algorithms

International audienceWe study the update of the distribution in Estimation of Distribution Algorithms, and show that a simple modification leads to unbiased estimates of the optimum. The simple modification (based on a proper reweighting of estimates) leads to a strongly improved behavior in front of premature convergence

Bias and variance in continuous EDA

International audienceEstimation of Distribution Algorithms are based on statistical estimates. We show that when combining classical tools from statistics, namely bias/variance decomposition, reweighting and quasi-randomization, we can strongly improve the convergence rate. All modifications are easy, compliant with most algorithms, and experimentally very efficient in particular in the parallel case (large offsprings)

Slightly beyond Turing-Computability for studying Genetic Programming

International audienceInspired by genetic programming (GP), we study iterative algorithms for non-computable tasks and compare them to naive models. This framework justifies many practical standard tricks from GP and also provides complexity lower-bounds which justify the computational cost of GP thanks to the use of Kolmogorov's complexity in bounded time

How entropy-theorems can show that approximating high-dim Pareto-fronts is too hard

It is empirically established that multiobjective evolutionary algorithms do not scale well with the number of conflicting objectives. We here show that the convergence rate of any comparison-based multi-objective algorithm, for the Hausdorff distance, is not much better than the convergence rate of the random search, unless the number of objectives is very moderate, in a framework in which the stronger assumption is that the objectives have conflicts. Our conclusions are (i) the relevance of the number of conflicting objectives (ii) the relevance of random-search-based criterions (iii) the very-hardness of more than 3- objectives optimization (iv) some hints about new cross-over operators

On the hardness of offline multiobjective optimization

International audienceIt is empirically established that multiobjective evolutionary algorithms do not scale well with the number of conflicting objectives. We here show that the convergence rate of all comparison-based multiobjective algorithms, for the Hausdorff distance, is not much better than the convergence rate of the random search, unless the number of objectives is very moderate, in a framework in which the stronger assumptions are (i) that the objectives are conflicting (ii) that lower bounding the computational cost by the number of comparisons is a good model. Our conclusions are (i) the relevance of the number of conflicting objectives (ii) the relevance of criteria based on comparisons with random-search for multi-objective optimization (iii) the very-hardness of more than 3- objectives optimization (iv) some hints about cross-over operators

Conditionning, halting criteria and choosing lambda

International audienceWe show the convergence of 1+ lambda-ES with standard step-size update-rules on a large family of fitness functions without any convexity assumption or quasi-convexity assumptions ([5, 6]). The result provides a rule for choosing lambda and shows the consistency of halting criteria based on thresholds on the step-size. The family of functions under work is defined through a conditionnumber that generalizes usual condition-numbers in a manner that only depends on level-sets. We consider that the definition of this conditionnumber is the relevant one for evolutionary algorithms; in particular, global convergence results without convexity or quasi-convexity assumptions are proved when this condition-number is finite

Exploration vs Exploitation vs Safety: Risk-averse Multi-Armed Bandits

Motivated by applications in energy management, this paper presents the Multi-Armed Risk-Aware Bandit (MARAB) algorithm. With the goal of limiting the exploration of risky arms, MARAB takes as arm quality its conditional value at risk. When the user-supplied risk level goes to 0, the arm quality tends toward the essential infimum of the arm distribution density, and MARAB tends toward the MIN multi-armed bandit algorithm, aimed at the arm with maximal minimal value. As a first contribution, this paper presents a theoretical analysis of the MIN algorithm under mild assumptions, establishing its robustness comparatively to UCB. The analysis is supported by extensive experimental validation of MIN and MARAB compared to UCB and state-of-art risk-aware MAB algorithms on artificial and real-world problems.Comment: 16 page