Fast and efficient incremental learning for high-dimensional movement systems

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 requires 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 linear function approximation. The outstanding properties 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 information to avoid interference problems, iv) has a computational complexity that is linear in the number of inputs, and v) can deal with a large number of possibly redundant 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 knowledge, this is the first incremental neural network learning method to combine all these properties and that is well suited for complex online learning problems in robotics