An adaptive online machine learning method based on a robust optimal control approach

Abstract

Reproducing kernel Hilbert space (RKHS) based models are promisingones for image processing, function approximation, patternrecognition, data mining problems and also have shown theireffectiveness in the system identification of nonlinear stochasticdynamical systems. In this paper, a novel control approach to theonline learning (regression) problems of RKHS based models isstudied in order to develop efficient algorithms with real time andadaptive parameter updates. To this aim, the learning 问题 forstochastic dynamical systems is reasonably translated into an outputfeedback control 问题 for discrete time varying linear dynamicalsystems with bounded random disturbances by some established newresults for RKHS, and an adaptive robust control algorithm istherefore developed for the learning 问题 using the robustoptimal model predictive control techniques. Compared with theexisting online kernel learning methods, the proposed one canrealize real time model parameter update without introducing anydata window principle, pruning technique, adjusting of learningsteps and any assumptions on random noise to achieve accurate onlinemodeling performance for stochastic dynamics with abrupt changes,and meanwhile guarantee the fast and robust convergence. Moreover, thisstudy could be the first attempt to use a kernel method to tackle theonline learning problems from the perspective of robustoptimal control theory. And under the proposed learning framework,existing well established control techniques can be potentiallyutilized to develop new robust learning methods, resultantly somenovel insight for kernel learning theory is provided as well.Theoretical analysis, numeral examples and comparisons are alsogiven to demonstrate our results.