Evolving Complexity in Prediction Games

To study open-ended coevolution, we define a complexity metric over interacting finite state machines playing formal language prediction games, and study the dynamics of populations under competitive and cooperative interactions. In the past purely competitive and purely cooperative interactions have been studied extensively, but neither can successfully and continuously drive an arms race. We present quantitative results using this complexity metric and analyze the causes of varying rates of complexity growth across different types of interactions. We find that while both purely competitive and purely cooperative coevolution are able to drive complexity growth above the rate of genetic drift, mixed systems with both competitive and cooperative interactions achieve significantly higher evolved complexity.

[1]  Dilip Mookherjee,et al.  Learning behavior in an experimental matching pennies game , 1994 .

[2]  John E. Hopcroft,et al.  An n log n algorithm for minimizing states in a finite automaton , 1971 .

[3]  Kristian Lindgren,et al.  Evolutionary phenomena in simple dynamics , 1992 .

[4]  Melanie Mitchell,et al.  Complexity - A Guided Tour , 2009 .

[5]  C. Adami,et al.  Evolution of Biological Complexity , 2000, Proc. Natl. Acad. Sci. USA.

[6]  R. Gibbons Game theory for applied economists , 1992 .

[7]  Sheng Yu,et al.  State Complexity of Regular Languages , 2001, J. Autom. Lang. Comb..

[8]  Yoshua Bengio,et al.  Generative Adversarial Nets , 2014, NIPS.

[9]  Hector Zenil,et al.  Complexity Measurement Based on Information Theory and Kolmogorov Complexity , 2015, Artificial Life.

[10]  Christoph Adami,et al.  Sequence complexity in Darwinian evolution , 2002, Complex..

[11]  Pieter Abbeel,et al.  InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets , 2016, NIPS.

[12]  Thomas S. Ray,et al.  Evolution, complexity, entropy and artificial reality , 1994 .

[13]  A. Shiryayev On Tables of Random Numbers , 1993 .

[14]  Peter J. Angeline,et al.  An evolutionary algorithm that constructs recurrent neural networks , 1994, IEEE Trans. Neural Networks.

[15]  J. Pollack,et al.  Challenges in coevolutionary learning: arms-race dynamics, open-endedness, and medicocre stable states , 1998 .

[16]  Martín Abadi,et al.  Learning to Protect Communications with Adversarial Neural Cryptography , 2016, ArXiv.

[17]  Wojciech Zaremba,et al.  Improved Techniques for Training GANs , 2016, NIPS.

[18]  Jean-Arcady Meyer,et al.  Coevolving Communicative Behavior in a Linear Pursuer-Evader Game , 1998 .