Relationships between Internal and External Metrics in Co-evolution

Popovici, Elena; Jong, Kenneth De

doi:10.1109/cec.2005.1555046

Cited by 11 publications

(11 citation statements)

References 6 publications

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“…This technique was first introduced in (Popovici and De Jong, 2004) and has been improved since then. We have already successfully used it to gain insight into the way co-evolutionary algorithms work, both in competitive (Popovici and De Jong, 2005b) and cooperative setups (Popovici and De Jong, 2005a;Popovici and De Jong, 2005c). In this paper we describe this technique and use it to extend our previous results.…”

Section: The Importance Of Co-evolutionary Dynamicsmentioning

confidence: 87%

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The dynamics of the best individuals in co-evolution

Popovici

Jong

2006

Nat Comput

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Abstract.There continues to be a growing interest in the use of co-evolutionary algorithms to solve difficult computational problems. Their performance however has varied widely from good to disappointing. The main reason for this is that co-evolutionary systems can display quite complex phenomena. Therefore, in order to efficiently use co-evolutionary algorithms for problem solving, one must have a good understanding of their dynamical behavior. To build such understanding, we have constructed a methodology for analyzing co-evolutionary dynamics based on trajectories of bestof-generation individuals. We applied this methodology to gain insights into how to tune certain algorithm parameters in order to improve performance.

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Section: The Importance Of Co-evolutionary Dynamicsmentioning

confidence: 87%

“…Additionally, although this paper has focused on cooperative setups, our previous work (Popovici and De Jong, 2004;Popovici and De Jong, 2005b) showed that the methods described here can be used to gain insights into competitive co-evolution as well.…”

Section: Discussionmentioning

confidence: 99%

The dynamics of the best individuals in co-evolution

Popovici

Jong

2006

Nat Comput

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“…Despite their similarity in framework, co-evolutionary learning and EAs are fundamentally different in how the fitness of a solution is assigned, leading to significantly different outcomes when applied to similar problems (e.g., different search behaviors on the space of solutions [7,8]). EAs are often viewed and constructed in terms of an optimization context [4,5], whereby an absolute fitness function is required to assign the fitness value to a solution that is objective (fitness value for a solution is always the same regardless of the context).…”

Section: Introductionmentioning

confidence: 99%

“…For such problems, continued use of an inappropriate fitness function will often bias the search to solutions that do not reflect the underlying properties of the problem, leading to suboptimal solutions [12]. Even if a fitness function can be formulated, it may not be able to evaluate and differentiate between individual solutions to provide some gradient to direct the search when using EAs [8,13]. One such problem that is difficult to solve using EAs, but can be naturally framed in co-evolutionary learning, is the problem of game-playing [2,3,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Measuring Generalization Performance in Coevolutionary Learning

Chong¹,

Tiňo²,

Yao³

2008

IEEE Trans. Evol. Computat.

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Co-evolutionary learning involves a training process where training samples are instances of solutions that interact strategically to guide the evolutionary (learning) process. One main research issue is with the generalization performance, i.e., the search for solutions (e.g., input-output mappings) that best predict the required output for any new input that has not been seen during the evolutionary process. However, there is currently no such framework for determining the generalization performance in co-evolutionary learning even though the notion of generalization is well-understood in machine learning. In this paper, we introduce a theoretical framework to address this research issue. We present the framework in terms of game-playing although our results are more general. Here, a strategy's generalization performance is its average performance against all test strategies. Given that the true value may not be determined by solving analytically a closed-form formula and is computationally prohibitive, we propose an estimation procedure that computes the average performance against a small sample of random test strategies instead. We perform a mathematical analysis to provide a statistical claim on the accuracy of our estimation procedure, which can be further improved by performing a second estimation on the variance of the random variable. For game-playing, it is well-known that one is more interested in the generalization performance against a biased and diverse sample of "good" test strategies. We introduce a simple approach to obtain such a test sample through the multiple partial enumerative search of the strategy space that does not require human expertise and is generally applicable to a wide range of domains. We illustrate the generalization framework on the co-evolutionary learning of the iterated prisoner's dilemma (IPD) games. We investigate two definitions of generalization performance for the IPD game based on different performance criteria, e.g., in terms of the number of wins based on individual outcomes and in terms of average payoff. We show that a small sample of test strategies can be used to estimate the generalization performance. We also show that the generalization performance using a biased and diverse set of "good" test strategies is lower compared to the unbiased case for the IPD game. This is the first time that generalization is defined and analyzed rigorously in co-evolutionary learning. The framework allows the evaluation of the generalization performance of any co-evolutionary learning system quantitatively.

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“…For example, early coevolutionary learning systems are implemented using coevolutionary algorithms derived from EAs [11], [13]. However, coevolutionary learning and EAs are fundamentally different in how the fitness of a solution is assigned, which may lead to significantly different outcomes when they are applied to similar problems (different search behaviors on the space of solutions) [14], [15]. Classical EAs are formulated in the context of optimization [3], [5], [6], where an absolute fitness function is used to assign fitness values to solutions.…”

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confidence: 99%

Relationship Between Generalization and Diversity in Coevolutionary Learning

Chong

Tiňo

Yao

2009

IEEE Trans. Comput. Intell. AI Games

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Abstract-Games have long played an important role in the development and understanding of coevolutionary learning systems. In particular, the search process in coevolutionary learning is guided by strategic interactions between solutions in the population, which can be naturally framed as game playing. We study two important issues in coevolutionary learning-generalization performance and diversity-using games. The first one is concerned with the coevolutionary learning of strategies with high generalization performance, that is, strategies that can outperform against a large number of test strategies (opponents) that may not have been seen during coevolution. The second one is concerned with diversity levels in the population that may lead to the search of strategies with poor generalization performance. It is not known if there is a relationship between generalization and diversity in coevolutionary learning. This paper investigates whether there is such a relationship in coevolutionary learning through a detailed empirical study. We systematically investigate the impact of various diversity maintenance approaches on the generalization performance of coevolutionary learning quantitatively using case studies. The problem of the iterated prisoner's dilemma (IPD) game is considered. Unlike past studies, we can measure both the generalization performance and the diversity level of the population of evolved strategies. Results from our case studies show that the introduction and maintenance of diversity do not necessarily lead to the coevolutionary learning of strategies with high generalization performance. However, if individual strategies can be combined (e.g., using a gating mechanism), there is the potential of exploiting diversity in coevolutionary learning to improve generalization performance. Specifically, when the introduction and maintenance of diversity lead to a speciated population during coevolution, where each specialist strategy is capable of outperforming different opponents, the population as a whole can have a significantly higher generalization performance compared to individual strategies.

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Relationships between Internal and External Metrics in Co-evolution

Cited by 11 publications

References 6 publications

The dynamics of the best individuals in co-evolution

The dynamics of the best individuals in co-evolution

Measuring Generalization Performance in Coevolutionary Learning

Relationship Between Generalization and Diversity in Coevolutionary Learning

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