Abstract
Locally weighted learning (LWL) is a class of techniques from nonparametric statistics that provides useful representations and training algorithms for learning about complex phenomena during autonomous adaptive control of robotic systems. This paper introduces several LWL algorithms that have been tested successfully in real-time learning of complex robot tasks. We discuss two major classes of LWL, memory-based LWL and purely incremental LWL that does not need to remember any data explicitly. In contrast to the traditional belief that LWL methods cannot work well in high-dimensional spaces, we provide new algorithms that have been tested on up to 90 dimensional learning problems. The applicability of our LWL algorithms is demonstrated in various robot learning examples, including the learning of devil-sticking, pole-balancing by a humanoid robot arm, and inverse-dynamics learning for a seven and a 30 degree-of-freedom robot. In all these examples, the application of our statistical neural networks techniques allowed either faster or more accurate acquisition of motor control than classical control engineering.
Similar content being viewed by others
References
S. Schaal, “Is imitation learning the route to humanoid robots?” Trends in Cognitive Sciences, vol. 3, pp. 233–242, 1999.
C.M. Bishop, Neural Networks for Pattern Recognition, Oxford University Press: New York, 1995.
C.K.I. Williams and C.E. Rasmussen, “Gaussian processes for regression,” in Advances in Neural Information Processing Systems, vol. 8, edited by D.S. Touretzky, M.C. Mozer, and M.E. Hasselmo, MIT Press: Cambridge, MA, pp. 514–520, 1996.
V.N. Vapnik, Estimation of Dependences Based on Empirical Data, Springer: Berlin, 1982.
C. Cortes and V. Vapnik, “Support vector networks,” Machine Learning, vol. 20, pp. 273–297, 1995.
V. Vapnik, S. Golowich, and A. Smola, “Support vector method for function approximation, regression estimation, and signal processing,” in Advances in Neural Information Processing Systems, vol. 9, edited by M. Mozer, M.I. Jordan, and T. Petsche, MIT Press: Cambridge, MA, pp. 281–287, 1996.
S. Schaal and C.G. Atkeson, “Constructive incremental learning from only local information,” Neural Comput, vol. 10, pp. 2047–2084, 1998.
C.G. Atkeson and S. Schaal, “Memory-based neural networks for robot learning,” Neurocomputing, vol. 9, pp. 1–27, 1995.
W.S. Cleveland and C. Loader, Smoothing by Local Regression: Principles and Methods, AT&T Bell Laboratories: Murray Hill, NY, 1995.
T.J. Hastie and R.J. Tibshirani, “Nonparametric regression and classification: Part I: Nonparametric regression,” in From Statistics to Neural Networks: Theory and Pattern Recognition Applications, edited by V. Cherkassky, J.H. Friedman, and H. Wechsler, ASI Proceedings, Subseries F, Computer and Systems Sciences, Springer: Berlin, pp. 120–143, 1994.
C.G. Atkeson, A.W. Moore, and S. Schaal, “Locally weighted learning,” Artificial Intelligence Review, vol. 11, pp. 11–73, 1997.
C.G. Atkeson, A.W. Moore, and S. Schaal, “Locally weighted learning for control,” Artificial Intelligence Review, vol. 11, pp. 75–113, 1997.
D. Aha, “Lazy learning,” Artificial Intelligence Review, vol. 11, no. 1–5, pp. 325–337, 1997.
L. Ljung and T. Söderström, Theory and Practice of Recursive Identification, MIT Press: Cambridge, MA, 1986.
W.S. Cleveland, “Robust locally weighted regression and smoothing scatterplots,” Journal of the American Statistical Association, vol. 74, pp. 829–836, 1979.
T. Hastie and C. Loader, “Local regression: Automatic kernel carpentry,” Statistical Science, vol. 8, pp. 120–143, 1993.
C.G. Atkeson, “Using local models to control movement,” in Advances in Neural Information Processing Systems, vol. 1, edited by D. Touretzky, Morgan Kaufmann: San Mateo, CA, pp. 157–183, 1989.
C.G. Atkeson, “Memory-based approaches to approximating continuous functions,” in Nonlinear Modeling and Forecasting, edited by M. Casdagli and S. Eubank, Addison Wesley: Redwood City, CA, pp. 503–521, 1992.
A.W. Moore, “Efficient memory-based learning for robot control,” Computer Laboratory, University of Cambridge, October 1990.
D.G. Lowe, “Similarity metric learning for a variable-kernel classifier,” Neural Comput, vol. 7, pp. 72–85, 1995.
H. Wold, “Soft modeling by latent variables: The nonlinear iterative partial least squares approach,” in Perspectives in Probability and Statistics, Papers in Honour of M.S. Bartlett, edited by J. Gani, Academic Press: London, pp. 520–540, 1975.
I.E. Frank and J.H. Friedman, “Astatistical viewof some chemometric regression tools,” Technometrics, vol. 35, pp. 109–135, 1993.
S. Schaal, S.Vijayakumar, and C.G. Atkeson, “Local dimensionality reduction,” in Advances in Neural Information Processing Systems, vol. 10, edited by M.I. Jordan, M.J. Kearns, and S.A. Solla, MIT Press: Cambridge, MA, pp. 633–639, 1998.
S. Vijayakumar and S. Schaal, “Locally weighted projection regression: An O(n) algorithm for incremental real time learning in high dimensional spaces,” in Proceedings of the Seventeenth International Conference on Machine Learning 2000 (ICML 2000), Stanford, CA.
W.P. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, Numerical Recipes in C—“The Art of Scientific Computing,” Press Syndiacate University of Cambridge: Cambridge, MA, 1989.
M. Kawato, “Internal models for motor control and trajectory planning,” Curr. Opin. Neurobiol, vol. 9, pp. 718–727, 1999.
D.M. Wolpert, R.C. Miall, and M. Kawato, “Internal models in the cerebellum,” Trends in Cognitive Sciences, vol. 2, pp. 338–347, 1998.
S. Schaal and C.G. Atkeson, “Robot juggling: An implementation of memory-based learning,” Control Systems Magazine, vol. 14, pp. 57–71, 1994.
P. Dyer and S.R. McReynolds, The Computation and Theory of Optimal Control, Academic Press: New York, 1970.
J.J. Craig, Introduction to Robotics, Addison-Wesley: Reading, MA, 1986.
C.H. An, C.G. Atkeson, and J.M. Hollerbach, Model-Based Control of a Robot Manipulator, MIT Press: Cambridge, MA, 1988.
J. Baillieul and D.P. Martin, “Resolution of kinematic redundancy,” in Proceedings of Symposia in Applied Mathematics, American Mathematical Society, pp. 49–89, 1990.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schaal, S., Atkeson, C.G. & Vijayakumar, S. Scalable Techniques from Nonparametric Statistics for Real Time Robot Learning. Applied Intelligence 17, 49–60 (2002). https://doi.org/10.1023/A:1015727715131
Issue Date:
DOI: https://doi.org/10.1023/A:1015727715131