arXiv subjects

Michael Emmerich

Publications and source records attributed to Michael Emmerich.

25 records · Page 2Linked to original sources

arXiv2018

Assessing the Potential of Classical Q-learning in General Game Playing

After the recent groundbreaking results of AlphaGo and AlphaZero, we have seen strong interests in deep reinforcement learning and artificial general intelligence (AGI) in game playing. However, deep learning is resource-intensive and the theory is not yet well developed. For small games, simple classical table-based Q-learning might still be the algorithm of choice. General Game Playing (GGP) provides a good testbed for reinforcement learning to research AGI. Q-learning is one of the canonical reinforcement learning methods, and has been used by (Banerjee $\&$ Stone, IJCAI 2007) in GGP. In this paper we implement Q-learning in GGP for three small-board games (Tic-Tac-Toe, Connect Four, Hex)\footnote{source code: https://github.com/wh1992v/ggp-rl}, to allow comparison to Banerjee et al.. We find that Q-learning converges to a high win rate in GGP. For the $ε$-greedy strategy, we propose a first enhancement, the dynamic $ε$ algorithm. In addition, inspired by (Gelly $\&$ Silver, ICML 2007) we combine online search (Monte Carlo Search) to enhance offline learning, and propose QM-learning for GGP. Both enhancements improve the performance of classical Q-learning. In this work, GGP allows us to show, if augmented by appropriate enhancements, that classical table-based Q-learning can perform well in small games.

cs.AI↗

arXiv2018

Monte Carlo Q-learning for General Game Playing

After the recent groundbreaking results of AlphaGo, we have seen a strong interest in reinforcement learning in game playing. General Game Playing (GGP) provides a good testbed for reinforcement learning. In GGP, a specification of games rules is given. GGP problems can be solved by reinforcement learning. Q-learning is one of the canonical reinforcement learning methods, and has been used by (Banerjee & Stone, IJCAI 2007) in GGP. In this paper we implement Q-learning in GGP for three small-board games (Tic-Tac-Toe, Connect Four, Hex), to allow comparison to Banerjee et al. As expected, Q-learning converges, although much slower than MCTS. Borrowing an idea from MCTS, we enhance Q-learning with Monte Carlo Search, to give QM-learning. This enhancement improves the performance of pure Q-learning. We believe that QM-learning can also be used to improve performance of reinforcement learning further for larger games, something which we will test in future work.

cs.AI↗

arXiv2017

An Ontology of Preference-Based Multiobjective Metaheuristics

User preference integration is of great importance in multi-objective optimization, in particular in many objective optimization. Preferences have long been considered in traditional multicriteria decision making (MCDM) which is based on mathematical programming. Recently, it is integrated in multi-objective metaheuristics (MOMH), resulting in focus on preferred parts of the Pareto front instead of the whole Pareto front. The number of publications on preference-based multi-objective metaheuristics has increased rapidly over the past decades. There already exist various preference handling methods and MOMH methods, which have been combined in diverse ways. This article proposes to use the Web Ontology Language (OWL) to model and systematize the results developed in this field. A review of the existing work is provided, based on which an ontology is built and instantiated with state-of-the-art results. The OWL ontology is made public and open to future extension. Moreover, the usage of the ontology is exemplified for different use-cases, including querying for methods that match an engineering application, bibliometric analysis, checking existence of combinations of preference models and MOMH techniques, and discovering opportunities for new research and open research questions.

cs.NE↗

arXiv2017

Cluster-based Kriging Approximation Algorithms for Complexity Reduction

Kriging or Gaussian Process Regression is applied in many fields as a non-linear regression model as well as a surrogate model in the field of evolutionary computation. However, the computational and space complexity of Kriging, that is cubic and quadratic in the number of data points respectively, becomes a major bottleneck with more and more data available nowadays. In this paper, we propose a general methodology for the complexity reduction, called cluster Kriging, where the whole data set is partitioned into smaller clusters and multiple Kriging models are built on top of them. In addition, four Kriging approximation algorithms are proposed as candidate algorithms within the new framework. Each of these algorithms can be applied to much larger data sets while maintaining the advantages and power of Kriging. The proposed algorithms are explained in detail and compared empirically against a broad set of existing state-of-the-art Kriging approximation methods on a well-defined testing framework. According to the empirical study, the proposed algorithms consistently outperform the existing algorithms. Moreover, some practical suggestions are provided for using the proposed algorithms.

cs.LG↗

arXiv2015

Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control

Constrained optimization of high-dimensional numerical problems plays an important role in many scientific and industrial applications. Function evaluations in many industrial applications are severely limited and no analytical information about objective function and constraint functions is available. For such expensive black-box optimization tasks, the constraint optimization algorithm COBRA was proposed, making use of RBF surrogate modeling for both the objective and the constraint functions. COBRA has shown remarkable success in solving reliably complex benchmark problems in less than 500 function evaluations. Unfortunately, COBRA requires careful adjustment of parameters in order to do so. In this work we present a new self-adjusting algorithm SACOBRA, which is based on COBRA and capable to achieve high-quality results with very few function evaluations and no parameter tuning. It is shown with the help of performance profiles on a set of benchmark problems (G-problems, MOPTA08) that SACOBRA consistently outperforms any COBRA algorithm with fixed parameter setting. We analyze the importance of the several new elements in SACOBRA and find that each element of SACOBRA plays a role to boost up the overall optimization performance. We discuss the reasons behind and get in this way a better understanding of high-quality RBF surrogate modeling.

math.OC↗

arXiv2014

Faster Computation of Expected Hypervolume Improvement

The expected improvement algorithm (or efficient global optimization) aims for global continuous optimization with a limited budget of black-box function evaluations. It is based on a statistical model of the function learned from previous evaluations and an infill criterion - the expected improvement - used to find a promising point for a new evaluation. The `expected improvement' infill criterion takes into account the mean and variance of a predictive multivariate Gaussian distribution. The expected improvement algorithm has recently been generalized to multiobjective optimization. In order to measure the improvement of a Pareto front quantitatively the gain in dominated (hyper-)volume is used. The computation of the expected hypervolume improvement (EHVI) is a multidimensional integration of a step-wise defined non-linear function related to the Gaussian probability density function over an intersection of boxes. This paper provides a new algorithm for the exact computation of the expected improvement to more than two objective functions. For the bicriteria case it has a time complexity in $O(n^2)$ with $n$ denoting the number of points in the current best Pareto front approximation. It improves previously known algorithms with time complexity $O(n^3 \log n)$. For tricriteria optimization we devise an algorithm with time complexity of $O(n^3)$. Besides discussing the new time complexity bounds the speed of the new algorithm is also tested empirically on test data. It is shown that further improvements in speed can be achieved by reusing data structures built up in previous iterations. The resulting numerical algorithms can be readily used in existing implementations of hypervolume-based expected improvement algorithms.

cs.DS↗

arXiv2013

Convex Hull-Based Multi-objective Genetic Programming for Maximizing ROC Performance

ROC is usually used to analyze the performance of classifiers in data mining. ROC convex hull (ROCCH) is the least convex major-ant (LCM) of the empirical ROC curve, and covers potential optima for the given set of classifiers. Generally, ROC performance maximization could be considered to maximize the ROCCH, which also means to maximize the true positive rate (tpr) and minimize the false positive rate (fpr) for each classifier in the ROC space. However, tpr and fpr are conflicting with each other in the ROCCH optimization process. Though ROCCH maximization problem seems like a multi-objective optimization problem (MOP), the special characters make it different from traditional MOP. In this work, we will discuss the difference between them and propose convex hull-based multi-objective genetic programming (CH-MOGP) to solve ROCCH maximization problems. Convex hull-based sort is an indicator based selection scheme that aims to maximize the area under convex hull, which serves as a unary indicator for the performance of a set of points. A selection procedure is described that can be efficiently implemented and follows similar design principles than classical hyper-volume based optimization algorithms. It is hypothesized that by using a tailored indicator-based selection scheme CH-MOGP gets more efficient for ROC convex hull approximation than algorithms which compute all Pareto optimal points. To test our hypothesis we compare the new CH-MOGP to MOGP with classical selection schemes, including NSGA-II, MOEA/D) and SMS-EMOA. Meanwhile, CH-MOGP is also compared with traditional machine learning algorithms such as C4.5, Naive Bayes and Prie. Experimental results based on 22 well-known UCI data sets show that CH-MOGP outperforms significantly traditional EMOAs.

cs.NE↗