Information geometry is a general framework of Riemannian manifolds with dual affine connections. Some manifolds (e.g. the manifold of an exponential family) have natural connections (e.g. e- and m-connections) with which the manifold is dually-flat. Conversely, a dually-flat structure can be introduced into a manifold from a potential function. This paper shows the case of quasi-additive algorithms as an example.
Information theory is another important tool in machine learning. Many of its applications consider information-theoretic quantities such as the entropy and the mutual information, but few fully recognize the underlying essence of them. The asymptotic equipartition property is one of the essence in information theory.
This paper gives an example of the property in a Markov decision process and shows how it is related to return maximization in reinforcement learning.
- Riemannian Manifold
- Reinforcement Learning
- Independent Component Analysis
- Exponential Family
- Markov Chain Model
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Amari, S.I.: Differential-Geometrical Methods in Statistics. Lecture Notes in Statistics, vol. 28. Springer, Heidelberg (1985)
Amari, S.I., Nagaoka, H.: Methods of Information Geometry. Translations of Mathematical Monographs, vol. 191. AMS and Oxford Univ. Press, Oxford (2000)
Cover, T.M., Thomas, J.A.: Elements of Information Theory, 2nd edn. John Wiley and Sons, Inc., Hoboken (2006)
Grove, A.J., Littlestone, N., Schuurmans, D.: General convergence results for linear discriminant updates. Machine Learning 43(3), 173–210 (2001)
Ikeda, K.: Geometric properties of quasi-additive learning algorithms. IEICE Trans. Fundamentals E89-A(10), 2812–2817 (2006)
Suzuki, J.: A markov chain analysis on simple genetic algorithms. IEEE Trans. on Systems, Man and Cybernetics 25(4), 655–659 (1995)
Suzuki, J.: A further result on the markov chain model of genetic algorithms and its application to a simulated annealing-like strategy. IEEE Trans. on Systems, Man and Cybernetics, Part B, Cybernetics 28(1), 95–102 (1998)
Iwata, K., Ikeda, K., Sakai, H.: The asymptotic equipartition property in reinforcement learning and its relation to return maximization. Neural Networks 19(1), 62–75 (2006)
Iwata, K., Ikeda, K., Sakai, H.: A statistical property of multi-agent learning based on Markov decision process. IEEE Trans. on Neural Networks 17(4), 829–842 (2006)
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Ikeda, K., Iwata, K. (2008). Information Geometry and Information Theory in Machine Learning. In: Ishikawa, M., Doya, K., Miyamoto, H., Yamakawa, T. (eds) Neural Information Processing. ICONIP 2007. Lecture Notes in Computer Science, vol 4985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69162-4_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69159-4
Online ISBN: 978-3-540-69162-4