Model-based relative entropy stochastic search

Stochastic search algorithms are general black-box optimizers. Due to their ease of use and their generality, they have recently also gained a lot of attention in operations research, machine learning and policy search. Yet, these algorithms require a lot of evaluations of the objective, scale poorly with the problem dimension, are affected by highly noisy objective functions and may converge prematurely. To alleviate these problems, we introduce a new surrogate-based stochastic search approach. We learn simple, quadratic surrogate models of the objective function. As the quality of such a quadratic approximation is limited, we do not greedily exploit the learned models. The algorithm can be misled by an inaccurate optimum introduced by the surrogate. Instead, we use information theoretic constraints to bound the ‘distance’ between the new and old data distribution while maximizing the objective function. Additionally the new method is able to sustain the exploration of the search distribution to avoid premature convergence. We compare our method with state of art black-box optimization methods on standard uni-modal and multi-modal optimization functions, on simulated planar robot tasks and a complex robot ball throwing task. The proposed method considerably outperforms the existing approaches

Intensive Surrogate Model Exploitation in Self-adaptive Surrogate-assisted CMA-ES (saACM-ES)

International audienceThis paper presents a new mechanism for a better exploitation of surrogate models in the framework of Evolution Strategies (ESs). This mechanism is instantiated here on the self-adaptive surrogate-assisted Covariance Matrix Adaptation Evolution Strategy (saACM-ES), a recently proposed surrogate-assisted variant of CMA-ES. As well as in the original saACM-ES, the expensive function is optimized by exploiting the surrogate model, whose hyper-parameters are also optimized online. The main novelty concerns a more intensive exploitation of the surrogate model by using much larger population sizes for its optimization. The new variant of saACM-ES significantly improves the original saACM-ES and further increases the speed-up compared to the CMA-ES, especially on unimodal functions (e.g., on 20-dimensional Rotated Ellipsoid, saACM-ES is 6 times faster than aCMA-ES and almost by one order of magnitude faster than CMA-ES). The empirical validation on the BBOB-2013 noiseless testbed demonstrates the efficiency and the robustness of the proposed mechanism

Information theoretic stochastic search

The MAP-i Doctoral Programme in Informatics, of the Universities of Minho, Aveiro and PortoOptimization is the research field that studies the design of algorithms for finding the best solutions to problems we may throw at them. While the whole domain is practically important, the present thesis will focus on the subfield of continuous black-box optimization, presenting a collection of novel, state-of-the-art algorithms for solving problems in that class. In this thesis, we introduce two novel general-purpose stochastic search algorithms for black box optimisation. Stochastic search algorithms aim at repeating the type of mutations that led to fittest search points in a population. We can model those mutations by a stochastic distribution. Typically the stochastic distribution is modelled as a multivariate Gaussian distribution. The key idea is to iteratively change the parameters of the distribution towards higher expected fitness. However we leverage information theoretic trust regions and limit the change of the new distribution. We show how plain maximisation of the fitness expectation without bounding the change of the distribution is destined to fail because of overfitting and the results in premature convergence. Being derived from first principles, the proposed methods can be elegantly extended to contextual learning setting which allows for learning context dependent stochastic distributions that generates optimal individuals for a given context, i.e, instead of learning one task at a time, we can learn multiple related tasks at once. However, the search distribution typically uses a parametric model using some hand-defined context features. Finding good context features is a challenging task, and hence, non-parametric methods are often preferred over their parametric counter-parts. Therefore, we further propose a non-parametric contextual stochastic search algorithm that can learn a non-parametric search distribution for multiple tasks simultaneously.Otimização é área de investigação que estuda o projeto de algoritmos para encontrar as melhores soluções, tendo em conta um conjunto de critérios, para problemas complexos. Embora todo o domínio de otimização tenha grande importância, este trabalho está focado no subcampo da otimização contínua de caixa preta, apresentando uma coleção de novos algoritmos novos de última geração para resolver problemas nessa classe. Nesta tese, apresentamos dois novos algoritmos de pesquisa estocástica de propósito geral para otimização de caixa preta. Os algoritmos de pesquisa estocástica visam repetir o tipo de mutações que levaram aos melhores pontos de pesquisa numa população. Podemos modelar essas mutações por meio de uma distribuição estocástica e, tipicamente, a distribuição estocástica é modelada como uma distribuição Gaussiana multivariada. A ideia chave é mudar iterativamente os parâmetros da distribuição incrementando a avaliação. No entanto, alavancamos as regiões de confiança teóricas de informação e limitamos a mudança de distribuição. Deste modo, demonstra-se como a maximização simples da expectativa de “fitness”, sem limites da mudança da distribuição, está destinada a falhar devido ao “overfitness” e à convergência prematura resultantes. Sendo derivado dos primeiros princípios, as abordagens propostas podem ser ampliadas, de forma elegante, para a configuração de aprendizagem contextual que permite a aprendizagem de distribuições estocásticas dependentes do contexto que geram os indivíduos ideais para um determinado contexto. No entanto, a distribuição de pesquisa geralmente usa um modelo paramétrico linear em algumas das características contextuais definidas manualmente. Encontrar uma contextos bem definidos é uma tarefa desafiadora e, portanto, os métodos não paramétricos são frequentemente preferidos em relação às seus semelhantes paramétricos. Portanto, propomos um algoritmo não paramétrico de pesquisa estocástica contextual que possa aprender uma distribuição de pesquisa não-paramétrica para várias tarefas simultaneamente.FCT - Fundação para a Ciência e a Tecnologia. As well as fundings by European Union’s FP7 under EuRoC grant agreement CP-IP 608849 and by LIACC (UID/CEC/00027/2015) and IEETA (UID/CEC/00127/2015)