1,990 research outputs found
Regularized covariance estimation for weighted maximum likelihood policy search methods
Many episode-based (or direct) policy search algorithms, maintain a multivariate Gaussian distribution as search distribution over the parameter space of some objective function. One class of algorithms, such as episodic REPS, PoWER or PI2 uses, a weighted maximum likelihood estimate (WMLE) to update the mean and covariance matrix of this distribution in each iteration. However, due to high dimensionality of covariance matrices and limited number of samples, the WMLE is an unreliable estimator. The use of WMLE leads to over-fitted covariance estimates, and, hence the variance/entropy of the search distribution decreases too quickly, which may cause premature convergence. In order to alleviate this problem, the estimated covariance matrix can be regularized in different ways, for example by using a convex combination of the diagonal covariance estimate and the sample covariance estimate. In this paper, we propose a new covariance matrix regularization technique for policy search methods that uses the convex combination of the sample covariance matrix and the old covariance matrix used in last iteration. The combination weighting is determined by specifying the desired entropy of the new search distribution. With this mechanism, the entropy of the search distribution can be gradually decreased without damage from the maximum likelihood estimate
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)
Multilevel Weighted Support Vector Machine for Classification on Healthcare Data with Missing Values
This work is motivated by the needs of predictive analytics on healthcare
data as represented by Electronic Medical Records. Such data is invariably
problematic: noisy, with missing entries, with imbalance in classes of
interests, leading to serious bias in predictive modeling. Since standard data
mining methods often produce poor performance measures, we argue for
development of specialized techniques of data-preprocessing and classification.
In this paper, we propose a new method to simultaneously classify large
datasets and reduce the effects of missing values. It is based on a multilevel
framework of the cost-sensitive SVM and the expected maximization imputation
method for missing values, which relies on iterated regression analyses. We
compare classification results of multilevel SVM-based algorithms on public
benchmark datasets with imbalanced classes and missing values as well as real
data in health applications, and show that our multilevel SVM-based method
produces fast, and more accurate and robust classification results.Comment: arXiv admin note: substantial text overlap with arXiv:1503.0625
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
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