ONLINE LEARNING OR TRACKING OFF DISCRETE INPUT-OUTPUT MAPS

This paper shows how a slowly time-varying nonlinear mapping can be le arned, if, for every possible input value, the corresponding estimated output value is stored in memory, (This representation form can be ca lled ''flash map,'' or pointwise representation, or look-up table,) Th us, very fast access to the mapping Is provided, The learning process is performed online during regular operation of the system and must av oid ''adaptation holes'' which could occur when some of the points are more frequently updated than other points, After analyzing the proble ms of previous approaches we show how radial basis function networks c an be modified for flash maps and present the tent roof tensioning alg orithm which is exclusively designed for learning flash maps, The conv ergence of the tent roof tensioning algorithm is proved, Finally, we c ompare the two approaches concluding that under the flash map restrict ion the tent roof tensioning algorithm is the better choice for learni ng low-dimensional mappings, if a polygonal approximation of the desir ed mapping is sufficiently smooth.