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)

Deriving and improving CMA-ES with Information geometric trust regions

CMA-ES is one of the most popular stochastic search algorithms. It performs favourably in many tasks without the need of extensive parameter tuning. The algorithm has many beneficial properties, including automatic step-size adaptation, efficient covariance updates that incorporates the current samples as well as the evolution path and its invariance properties. Its update rules are composed of well established heuristics where the theoretical foundations of some of these rules are also well understood. In this paper we will fully derive all CMA-ES update rules within the framework of expectation-maximisation-based stochastic search algorithms using information-geometric trust regions. We show that the use of the trust region results in similar updates to CMA-ES for the mean and the covariance matrix while it allows for the derivation of an improved update rule for the step-size. Our new algorithm, Trust-Region Covariance Matrix Adaptation Evolution Strategy (TR-CMA-ES) is fully derived from first order optimization principles and performs favourably in compare to standard CMA-ES algorithm

Osjetljivo kinetičko-spektrofotometrijsko odre|ivanje SbIII temeljeno na njegovu inhibitornome djelovanju na reakciju dekoloriranja indikatora

A method for rapid and accurate determination of trace quantities of SbIII was developed based on its inhibitory effect on the decolorizing reaction of methyl orange in the presence of bromate and bromide ions in acidic media. Decolorization of methyl orange by the reaction products was used to monitor the reaction spectrophotometrically at 525 nm. The method allows determination of antimony in the range 10–5000 μg dm–3. The relative standard deviation for ten determinations of 500 μg dm–3 antimony is 1.21 % and the detection limit of the method is 8.0 μg dm–3. The method is applied to the determination of antimony in natural water samples.Razvijena je metoda za brzo i precizno određivanje tragova SbIII temeljena na inhibitornome djelovanju na reakciju dekoloriranja metil oranža uz bromate i bromidne ione u kiselom mediju. Upotrebljeno je dekoloriranje metil oranža s reakcijskim produktima za praćenje reakcije spektrofotometrijski kod 525 nm. Predložena metoda dopušta određivanje antimona u koncentracijama od 10 do 5000 μg dm–3. Relativna standardna devijacija za deset određivanja uzoraka od 500 μg dm–3 bila je 1.21%, a granica osjetljivosti metode bila je 8.0 μg dm–3. Metoda je uporabljena za određivanje antimona u uzorcima prirodnih voda

Contextual covariance matrix adaptation evolutionary strategies

Many stochastic search algorithms are designed to optimize a fixed objective function to learn a task, i.e., if the objective function changes slightly, for example, due to a change in the situation or context of the task, relearning is required to adapt to the new context. For instance, if we want to learn a kicking movement for a soccer robot, we have to relearn the movement for different ball locations. Such relearning is undesired as it is highly inefficient and many applications require a fast adaptation to a new context/situation. Therefore, we investigate contextual stochastic search algorithms that can learn multiple, similar tasks simultaneously. Current contextual stochastic search methods are based on policy search algorithms and suffer from premature convergence and the need for parameter tuning. In this paper, we extend the well known CMA-ES algorithm to the contextual setting and illustrate its performance on several contextual tasks. Our new algorithm, called contextual CMAES, leverages from contextual learning while it preserves all the features of standard CMA-ES such as stability, avoidance of premature convergence, step size control and a minimal amount of parameter tuning.This research was funded by European Union’s FP7 un- der EuRoC grant agreement CP-IP 608849 and LIACC (UID/CEC/00027/2015) and IEETA (UID/CEC/00127/2015) and also partially was funded by PARC.info:eu-repo/semantics/publishedVersio