Evolutionary game theoretic approach for modeling civil violence
IEEE Transactions on Evolutionary Computation
IEEE Transactions on Evolutionary Computation
Coevolution in a large search space using resource-limited nash memory
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Co-evolution of optimal agents for the alternating offers bargaining game
EvoApplicatons'10 Proceedings of the 2010 international conference on Applications of Evolutionary Computation - Volume Part I
The effects of diversity maintenance on coevolution for an intransitive numbers problem
AI'11 Proceedings of the 24th international conference on Advances in Artificial Intelligence
Evaluating coevolution on a multimodal problem
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Unpacking and understanding evolutionary algorithms
WCCI'12 Proceedings of the 2012 World Congress conference on Advances in Computational Intelligence
A multimodal problem for competitive coevolution
AI'12 Proceedings of the 25th Australasian joint conference on Advances in Artificial Intelligence
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Coevolutionary 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 coevolutionary 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 coevolutionary 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 coevolutionary learning. The framework allows the evaluation of the generalization performance of any coevolutionary learning system quantitatively.