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Bayesian MultiScale Optimistic Optimization
"... Bayesian optimization is a powerful global optimization technique for expensive blackbox functions. One of its shortcomings is that it requires auxiliary optimization of an acquisition function at each iteration. This auxiliary optimization can be costly and very hard to carry out in practice. M ..."
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Bayesian optimization is a powerful global optimization technique for expensive blackbox functions. One of its shortcomings is that it requires auxiliary optimization of an acquisition function at each iteration. This auxiliary optimization can be costly and very hard to carry out in practice. Moreover, it creates serious theoretical concerns, as most of the convergence results assume that the exact optimum of the acquisition function can be found. In this paper, we introduce a new technique for efficient global optimization that combines Gaussian process confidence bounds and treed simultaneous optimistic optimization to eliminate the need for auxiliary optimization of acquisition functions. The experiments with global optimization benchmarks and a novel application to automatic information extraction demonstrate that the resulting technique is more efficient than the two approaches from which it draws inspiration. Unlike most theoretical analyses of Bayesian optimization with Gaussian processes, our finitetime convergence rate proofs do not require exact optimization of an acquisition function. That is, our approach eliminates the unsatisfactory assumption that a difficult, potentially NPhard, problem has to be solved in order to obtain vanishing regret rates. 1
Simple regret for infinitely many armed bandits. arXiv:1505.04627, http://arxiv.org/abs/1505.04627, ArXiv eprints,,
, 2015
"... Abstract We consider a stochastic bandit problem with infinitely many arms. In this setting, the learner has no chance of trying all the arms even once and has to dedicate its limited number of samples only to a certain number of arms. All previous algorithms for this setting were designed for mini ..."
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Abstract We consider a stochastic bandit problem with infinitely many arms. In this setting, the learner has no chance of trying all the arms even once and has to dedicate its limited number of samples only to a certain number of arms. All previous algorithms for this setting were designed for minimizing the cumulative regret of the learner. In this paper, we propose an algorithm aiming at minimizing the simple regret. As in the cumulative regret setting of infinitely many armed bandits, the rate of the simple regret will depend on a parameter β characterizing the distribution of the nearoptimal arms. We prove that depending on β, our algorithm is minimax optimal either up to a multiplicative constant or up to a log(n) factor. We also provide extensions to several important cases: when β is unknown, in a natural setting where the nearoptimal arms have a small variance, and in the case of unknown time horizon.
Aggregating Optimistic Planning Trees for Solving Markov Decision Processes
, 2014
"... Aggregating optimistic planning trees for solving markov decision processes ..."
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Aggregating optimistic planning trees for solving markov decision processes
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, 2015
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Simple regret for infinitely many armed bandits
LearningBased Modular Indirect Adaptive Control for a Class of Nonlinear Systems
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Blackbox optimization of noisy functions with unknown smoothness
"... Abstract We study the problem of blackbox optimization of a function f of any dimension, given function evaluations perturbed by noise. The function is assumed to be locally smooth around one of its global optima, but this smoothness is unknown. Our contribution is an adaptive optimization algorit ..."
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Abstract We study the problem of blackbox optimization of a function f of any dimension, given function evaluations perturbed by noise. The function is assumed to be locally smooth around one of its global optima, but this smoothness is unknown. Our contribution is an adaptive optimization algorithm, POO or parallel optimistic optimization, that is able to deal with this setting. POO performs almost as well as the best known algorithms requiring the knowledge of the smoothness. Furthermore, POO works for a larger class of functions than what was previously considered, especially for functions that are difficult to optimize, in a very precise sense. We provide a finitetime analysis of POO's performance, which shows that its error after n evaluations is at most a factor of √ ln n away from the error of the best known optimization algorithms using the knowledge of the smoothness.
Improved Learning Complexity in Combinatorial Pure Exploration Bandits
"... Abstract We study the problem of combinatorial pure exploration in the stochastic multiarmed bandit problem. We first construct a new measure of complexity that provably characterizes the learning performance of the algorithms we propose for the fixed confidence and the fixed budget setting. We sh ..."
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Abstract We study the problem of combinatorial pure exploration in the stochastic multiarmed bandit problem. We first construct a new measure of complexity that provably characterizes the learning performance of the algorithms we propose for the fixed confidence and the fixed budget setting. We show that this complexity is never higher than the one in existing work and illustrate a number of configurations in which it can be significantly smaller. While in general this improvement comes at the cost of increased computational complexity, we provide a series of examples, including a planning problem, where this extra cost is not significant.