Abstract
We show that under reasonable conditions, online learning near a local minimum is similar to a multivariate Ornstein Uhlenbeck process. This implies that the parameter state oscillates randomly around the minimum point, with a Gaussian limiting distribution. We also develop a simple hypothesis test that detects Ornstein Uhlenbeck properties without storing the history of the learning process.
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Hassoun, M. H.: Fundamentals of Artificial Neural Networks. MIT Press, 1995
B. Widrow M. E. Hoff (1960) ArticleTitleAdaptive switching circuits IRE WESCON Convention Record 4 94–104
Ripley, B. D.: Pattern Recognition and Neural Networks. Cambridge University Press, 1996.
G. Tesauro (1992) ArticleTitlePractical issues in temporal difference learning Machine Learning 8 257–277 Occurrence Handle0772.68075
Hastie T., Tibshirani R., Friedman J.: The Elements of Statistical Learning. Springer, 2001.
Øksendal, B.: Stochastic Differential Equations, an Introduction with Applications. Springer, 1998.
S. Schach (1971) ArticleTitleWeak convergence results for a class of multivariate markov processes The Annals of Mathematical Statistics 42 IssueID2 451–465 Occurrence Handle0215.53403 Occurrence Handle45 #4507
Protter P.: Stochastic Integration and Differential Equations, a New Approach. Springer, 1990
I. I. Gikhman A. V. Skorokhod (1969) Introduction to the Theory of Stochastic Processes Saunders Philadelphia
H.J. Kushner (1974) ArticleTitleOn the weak convergence of interpolated Markov chains to a diffusion The Annals of Probability 2 IssueID1 40–50 Occurrence Handle0285.60064 Occurrence Handle50 #14869
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Dahl, F.A. How Online Learning Approaches Ornstein Uhlenbeck Processes. Neural Process Lett 23, 121–131 (2006). https://doi.org/10.1007/s11063-005-3669-5
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DOI: https://doi.org/10.1007/s11063-005-3669-5