Fast and efficient incremental learning for high-dimensional movement systems

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Abstract
⊕ Kawato Dynamic Brain Project (ERATO/JST), 2-2 Hikaridai, Seika-cho, Soraku-gun, 619-02 Kyoto, Japan We introduce a new algorithm, Locally Weighted Projection Regression (LWPR), for incremental real-time learning of nonlinear functions, as particularly useful for problems of autonomous real-time robot control that re- quires internal models of dynamics, kinematics, or other functions. At its core, LWPR uses locally linear models, spanned by a small number of univariate regressions in selected directions in input space, to achieve piecewise lin- ear function approximation. The most outstanding proper- ties of LWPR are that it i) learns rapidly with second order learning methods based on incremental training, ii) uses statistically sound stochastic cross validation to learn iii) adjusts its local weighting kernels based on only local in- formation to avoid interference problems, iv) has a com- putational complexity that is linear in the number of inputs, and v) can deal with a large number of—possibly redun- dant and/or irrelevant—inputs, as shown in evaluations with up to 50 dimensional data sets for learning the inverse dynamics of an anthropomorphic robot arm. To our knowl- edge, this is the first incremental neural network learning method to combine all these properties and that is well suited for complex on-line learning problems in robotics.

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