Dynamic characteristics of a continuous optimization method based on fictitious play theory

In this paper, we propose a continuous optimization algorithm based on fictitious play theory and investigate the dynamic characteristics of the proposed algorithm. Fictitious play is a model for a learning rule in evolutionary game theory, and it can be used as an optimization method when all playe...

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Veröffentlicht in:Journal of the Korean Physical Society Jg. 70; H. 9; S. 880 - 890
1. Verfasser: Lee, Chang-Yong
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Seoul The Korean Physical Society 01.05.2017
Springer Nature B.V
한국물리학회
Schlagworte:
Continuity (mathematics)
Dynamic characteristics
Evolutionary algorithms
Game theory
Machine learning
Mathematical and Computational Physics
Optimization
Optimization algorithms
Particle and Nuclear Physics
Physics
Physics and Astronomy
Players
Theoretical
물리학
Bayesian estimate
1/f noise
Continuous optimization algorithm
Fictitious play theory
Multifractal
ISSN:0374-4884, 1976-8524
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Zusammenfassung:In this paper, we propose a continuous optimization algorithm based on fictitious play theory and investigate the dynamic characteristics of the proposed algorithm. Fictitious play is a model for a learning rule in evolutionary game theory, and it can be used as an optimization method when all players have an identical utility function. In order to apply fictitious play to a continuous optimization algorithm, we consider two methods, equal width and equal frequency, of discretizing continuous values into a finite set of a player’s strategies. The equal-frequency method turns out to outperform the equal-width method in terms of minimizing inseparable functions. To understand the mechanism of the equal-frequency method, we investigate two important quantities, the mixed strategy and the best response, in the algorithm from the statistical physics viewpoint. We find that the dynamics of the mixed strategies can be described as a 1/ f noise. In addition, we adopt the set of best responses as the probability measure and find that the probability distribution of the set can be best characterized by a multifractal; moreover, the support of the measure has a fractal dimension. The dynamics of the proposed algorithm with equal-frequency discretization contains a complex and rich structure that can be related to the optimization mechanism.
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ISSN:0374-4884
1976-8524
DOI:10.3938/jkps.70.880