Self-Adaptive Surrogate-Assisted Covariance Matrix Adaptation Evolution Strategy

This paper presents a novel mechanism to adapt surrogate-assisted population-based algorithms. This mechanism is applied to ACM-ES, a recently proposed surrogate-assisted variant of CMA-ES. The resulting algorithm, saACM-ES, adjusts online the lifelength of the current surrogate model (the number of CMA-ES generations before learning a new surrogate) and the surrogate hyper-parameters. Both heuristics significantly improve the quality of the surrogate model, yielding a significant speed-up of saACM-ES compared to the ACM-ES and CMA-ES baselines. The empirical validation of saACM-ES on the BBOB-2012 noiseless testbed demonstrates the efficiency and the scalability w.r.t the problem dimension and the population size of the proposed approach, that reaches new best results on some of the benchmark problems.Comment: Genetic and Evolutionary Computation Conference (GECCO 2012) (2012

Maximum Likelihood-based Online Adaptation of Hyper-parameters in CMA-ES

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is widely accepted as a robust derivative-free continuous optimization algorithm for non-linear and non-convex optimization problems. CMA-ES is well known to be almost parameterless, meaning that only one hyper-parameter, the population size, is proposed to be tuned by the user. In this paper, we propose a principled approach called self-CMA-ES to achieve the online adaptation of CMA-ES hyper-parameters in order to improve its overall performance. Experimental results show that for larger-than-default population size, the default settings of hyper-parameters of CMA-ES are far from being optimal, and that self-CMA-ES allows for dynamically approaching optimal settings.Comment: 13th International Conference on Parallel Problem Solving from Nature (PPSN 2014) (2014

Alternative Restart Strategies for CMA-ES

This paper focuses on the restart strategy of CMA-ES on multi-modal functions. A first alternative strategy proceeds by decreasing the initial step-size of the mutation while doubling the population size at each restart. A second strategy adaptively allocates the computational budget among the restart settings in the BIPOP scheme. Both restart strategies are validated on the BBOB benchmark; their generality is also demonstrated on an independent real-world problem suite related to spacecraft trajectory optimization

Injecting External Solutions Into CMA-ES

This report considers how to inject external candidate solutions into the CMA-ES algorithm. The injected solutions might stem from a gradient or a Newton step, a surrogate model optimizer or any other oracle or search mechanism. They can also be the result of a repair mechanism, for example to render infeasible solutions feasible. Only small modifications to the CMA-ES are necessary to turn injection into a reliable and effective method: too long steps need to be tightly renormalized. The main objective of this report is to reveal this simple mechanism. Depending on the source of the injected solutions, interesting variants of CMA-ES arise. When the best-ever solution is always (re-)injected, an elitist variant of CMA-ES with weighted multi-recombination arises. When \emph{all} solutions are injected from an \emph{external} source, the resulting algorithm might be viewed as \emph{adaptive encoding} with step-size control. In first experiments, injected solutions of very good quality lead to a convergence speed twice as fast as on the (simple) sphere function without injection. This means that we observe an impressive speed-up on otherwise difficult to solve functions. Single bad injected solutions on the other hand do no significant harm.Comment: No. RR-7748 (2011

Black-Box Data-efficient Policy Search for Robotics

The most data-efficient algorithms for reinforcement learning (RL) in robotics are based on uncertain dynamical models: after each episode, they first learn a dynamical model of the robot, then they use an optimization algorithm to find a policy that maximizes the expected return given the model and its uncertainties. It is often believed that this optimization can be tractable only if analytical, gradient-based algorithms are used; however, these algorithms require using specific families of reward functions and policies, which greatly limits the flexibility of the overall approach. In this paper, we introduce a novel model-based RL algorithm, called Black-DROPS (Black-box Data-efficient RObot Policy Search) that: (1) does not impose any constraint on the reward function or the policy (they are treated as black-boxes), (2) is as data-efficient as the state-of-the-art algorithm for data-efficient RL in robotics, and (3) is as fast (or faster) than analytical approaches when several cores are available. The key idea is to replace the gradient-based optimization algorithm with a parallel, black-box algorithm that takes into account the model uncertainties. We demonstrate the performance of our new algorithm on two standard control benchmark problems (in simulation) and a low-cost robotic manipulator (with a real robot).Comment: Accepted at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2017; Code at http://github.com/resibots/blackdrops; Video at http://youtu.be/kTEyYiIFGP

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)