  There is a growing interest in using Kalman-filter models in brain modelling.
In turn, it is of considerable importance to make Kalman-filters amenable for
reinforcement learning. In the usual formulation of optimal control it is
computed off-line by solving a backward recursion. In this technical note we
show that slight modification of the linear-quadratic-Gaussian Kalman-filter
model allows the on-line estimation of optimal control and makes the bridge to
reinforcement learning. Moreover, the learning rule for value estimation
assumes a Hebbian form weighted by the error of the value estimation.
