Algorithm Portfolios for Noisy Optimization

Noisy optimization is the optimization of objective functions corrupted by noise. A portfolio of solvers is a set of solvers equipped with an algorithm selection tool for distributing the computational power among them. Portfolios are widely and successfully used in combinatorial optimization. In this work, we study portfolios of noisy optimization solvers. We obtain mathematically proved performance (in the sense that the portfolio performs nearly as well as the best of its solvers) by an ad hoc portfolio algorithm dedicated to noisy optimization. A somehow surprising result is that it is better to compare solvers with some lag, i.e., propose the current recommendation of best solver based on their performance earlier in the run. An additional finding is a principled method for distributing the computational power among solvers in the portfolio.Comment: in Annals of Mathematics and Artificial Intelligence, Springer Verlag, 201

Computational Intelligence Sequential Monte Carlos for Recursive Bayesian Estimation

Recursive Bayesian estimation using sequential Monte Carlos methods is a powerful numerical technique to understand latent dynamics of non-linear non-Gaussian dynamical systems. Classical sequential Monte Carlos suffer from weight degeneracy which is where the number of distinct particles collapse. Traditionally this is addressed by resampling, which effectively replaces high weight particles with many particles with high inter-particle correlation. Frequent resampling, however, leads to a lack of diversity amongst the particle set in a problem known as sample impoverishment. Traditional sequential Monte Carlo methods attempt to resolve this correlated problem however introduce further data processing issues leading to minimal to comparable performance improvements over the sequential Monte Carlo particle filter. A new method, the adaptive path particle filter, is proposed for recursive Bayesian estimation of non-linear non-Gaussian dynamical systems. Our method addresses the weight degeneracy and sample impoverishment problem by embedding a computational intelligence step of adaptive path switching between generations based on maximal likelihood as a fitness function. Preliminary tests on a scalar estimation problem with non-linear non-Gaussian dynamics and a non-stationary observation model and the traditional univariate stochastic volatility problem are presented. Building on these preliminary results, we evaluate our adaptive path particle filter on the stochastic volatility estimation problem. We calibrate the Heston stochastic volatility model employing a Markov chain Monte Carlo on six securities. Finally, we investigate the efficacy of sequential Monte Carlos for recursive Bayesian estimation of astrophysical time series. We posit latent dynamics for both regularized and irregular astrophysical time series, calibrating fifty-five quasar time series using the CAR(1) model. We find the adaptive path particle filter to statistically significantly outperform the standard sequential importance resampling particle filter, the Markov chain Monte Carlo particle filter and, upon Heston model estimation, the particle learning algorithm particle filter. In addition, from our quasar MCMC calibration we find the characteristic timescale τ to be first-order stable in contradiction to the literature though indicative of a unified underlying structure. We offer detailed analysis throughout, and conclude with a discussion and suggestions for future work

Population Statistics for Particle Swarm Optimization on Problems Subject to Noise

Particle Swarm Optimization (PSO) is a metaheuristic where a swarm of particles explores the search space of an optimization problem to find good solutions. However, if the problem is subject to noise, the quality of the resulting solutions significantly deteriorates. The literature has attributed such a deterioration to particles suffering from inaccurate memories and from the incorrect selection of their neighborhood best solutions. For both cases, the incorporation of noise mitigation mechanisms has improved the quality of the results, but the analyses beyond such improvements often fall short of empirical evidence supporting their claims in terms other than the quality of the results. Furthermore, there is not even evidence showing the extent to which inaccurate memories and incorrect selection affect the particles in the swarm. Therefore, the performance of PSO on noisy optimization problems remains largely unexplored. The overall goal of this thesis is to study the effect of noise on PSO beyond the known deterioration of its results in order to develop more efficient noise mitigation mechanisms. Based on the allocation of function evaluations by the noise mitigation mechanisms, we distinguish three groups of PSO algorithms as: single-evaluation, which sacrifice the accuracy of the objective values over performing more iterations; resampling-based, which sacrifice performing more iterations over better estimating the objective values; and hybrids, which merge methods from the previous two. With an empirical approach, we study and analyze the performance of existing and new PSO algorithms from each group on 20 large-scale benchmark functions subject to different levels of multiplicative Gaussian noise. Throughout the search process, we compute a set of 16 population statistics that measure different characteristics of the swarms and provide useful information that we utilize to design better PSO algorithms. Our study identifies and defines deception, blindness and disorientation as three conditions from which particles suffer in noisy optimization problems. The population statistics for different PSO algorithms reveal that particles often suffer from large proportions of deception, blindness and disorientation, and show that reducing these three conditions would lead to better results. The sensitivity of PSO to noisy optimization problems is confirmed and highlights the importance of noise mitigation mechanisms. The population statistics for single-evaluation PSO algorithms show that the commonly used evaporation mechanism produces too much disorientation, leading to divergent behaviour and to the worst results within the group. Two better algorithms are designed, the first utilizes probabilistic updates to reduce disorientation, and the second computes a centroid solution as the neighborhood best solution to reduce deception. The population statistics for resampling-based PSO algorithms show that basic resampling still leads to large proportions of deception and blindness, and its results are the worst within the group. Two better algorithms are designed to reduce deception and blindness. The first provides better estimates of the personal best solutions, and the second provides even better estimates of a few solutions from which the neighborhood best solutions are selected. However, an existing PSO algorithm is the best within the group as it strives to asymptotically minimize deception by sequentially reducing both blindness and disorientation. The population statistics for hybrid PSO algorithms show that they provide the best results thanks to a combined reduction of deception, blindness and disorientation. Amongst the hybrids, we find a promising algorithm whose simplicity, flexibility and quality of results questions the importance of overly complex methods designed to minimize deception. Overall, our research presents a thorough study to design, evaluate and tune PSO algorithms to address optimization problems subject to noise

Object Tracking

Object tracking consists in estimation of trajectory of moving objects in the sequence of images. Automation of the computer object tracking is a difficult task. Dynamics of multiple parameters changes representing features and motion of the objects, and temporary partial or full occlusion of the tracked objects have to be considered. This monograph presents the development of object tracking algorithms, methods and systems. Both, state of the art of object tracking methods and also the new trends in research are described in this book. Fourteen chapters are split into two sections. Section 1 presents new theoretical ideas whereas Section 2 presents real-life applications. Despite the variety of topics contained in this monograph it constitutes a consisted knowledge in the field of computer object tracking. The intention of editor was to follow up the very quick progress in the developing of methods as well as extension of the application

Langevin and Hamiltonian based Sequential MCMC for Efficient Bayesian Filtering in High-dimensional Spaces

Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm, also known as particle filtering. Nevertheless, this method tends to be inefficient when applied to high dimensional problems. In this paper, we focus on another class of sequential inference methods, namely the Sequential Markov Chain Monte Carlo (SMCMC) techniques, which represent a promising alternative to SMC methods. After providing a unifying framework for the class of SMCMC approaches, we propose novel efficient strategies based on the principle of Langevin diffusion and Hamiltonian dynamics in order to cope with the increasing number of high-dimensional applications. Simulation results show that the proposed algorithms achieve significantly better performance compared to existing algorithms

Preventing premature convergence and proving the optimality in evolutionary algorithms

http://ea2013.inria.fr//proceedings.pdfInternational audienceEvolutionary Algorithms (EA) usually carry out an efficient exploration of the search-space, but get often trapped in local minima and do not prove the optimality of the solution. Interval-based techniques, on the other hand, yield a numerical proof of optimality of the solution. However, they may fail to converge within a reasonable time due to their inability to quickly compute a good approximation of the global minimum and their exponential complexity. The contribution of this paper is a hybrid algorithm called Charibde in which a particular EA, Differential Evolution, cooperates with a Branch and Bound algorithm endowed with interval propagation techniques. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate its efficiency on a benchmark of highly multimodal problems, for which we provide previously unknown global minima and certification of optimality

Real-coded genetic algorithm particle filters for high-dimensional state spaces

This thesis successfully addresses the issues faced by particle filters in high-dimensional state-spaces by comparing them with genetic algorithms and then using genetic algorithm theory to address these issues. Sequential Monte Carlo methods are a class of online posterior density estimation algorithms that are suitable for non-Gaussian and nonlinear environments, however they are known to suffer from particle degeneracy; where the sample of particles becomes too sparse to approximate the posterior accurately. Various techniques have been proposed to address this issue but these techniques fail in high-dimensions. In this thesis, after a careful comparison between genetic algorithms and particle filters, we posit that genetic algorithm theoretic arguments can be used to explain the working of particle filters. Analysing the working of a particle filter, we note that it is designed similar to a genetic algorithm but does not include recombination. We argue based on the building-block hypothesis that the addition of a recombination operator would be able to address the sample impoverishment phenomenon in higher dimensions. We propose a novel real-coded genetic algorithm particle filter (RGAPF) based on these observations and test our hypothesis on the stochastic volatility estimation of financial stocks. The RGAPF successfully scales to higher-dimensions. To further strengthen our argument that whether building-block-hypothesis-like effects are due to the recombination operator, we compare the RGAPF with a mutation-only particle filter with an adjustable mutation rate that is set to equal the population-to-population variance of the RGAPF. The latter significantly and consistently performs better, indicating that recombination is having a subtle and significant effect that may be theoretically explained by genetic algorithm theory. After two successful attempts at validating our hypothesis we compare the performance of the RGAPF using different real-recombination operators. Observing the behaviour of the RGAPF under these recombination operators we propose a mean-centric recombination operator specifically for high-dimensional particle filtering. This recombination operator is successfully tested and compared with benchmark particle filters and a hybrid CMA-ES particle filter using simulated data and finally on real end-of-day data of the securities making up the FTSE-100 index. Each experiment is discussed in detail and we conclude with a brief description of the future direction of research

Algorithm Portfolios for Noisy Optimization: Compare Solvers Early

International audienceNoisy optimization is the optimization of objective functions corrupted by noise. A portfolio of algorithms is a set of algorithms equipped with an algorithm selection tool for distributing the compu- tational power among them. We study portfolios of noisy optimization solvers, show that different settings lead to dramatically different perfor- mances, obtain mathematically proved adaptivity by an ad hoc selection algorithm dedicated to noisy optimization. A somehow surprising result is that it is better to compare solvers with some lag; i.e., recommend the current recommendation of the best solver, selected from a comparison based on their recommendations earlier in the run

Computational intelligence approaches to robotics, automation, and control [Volume guest editors]

No abstract available