Online learning or tracking of discrete input-output maps

This paper shows how a slowly time-varying nonlinear mapping can be learned, if, for every possible input value, the corresponding estimated output value is stored in memory. This representation form can be called "flash map", or pointwise representation, or look-up table. Thus, very fast access to the mapping is provided. The learning process is performed online during regular operation of the system and must avoid "adaptation holes" which could occur when some of the points are more frequently updated than other points. After analyzing the problems of previous approaches we show how radial basis function networks can be modified for flash maps and present the tent roof tensioning algorithm which is exclusively designed for learning flash maps. The convergence of the tent roof tensioning algorithm is proved. Finally, we compare the two approaches concluding that under the flash map restriction the tent roof tensioning algorithm is the better choice for learning low-dimensional mappings, if a polygonal approximation of the desired mapping is sufficiently smooth.