1. A computer implemented method for generating a set of gain vectors with respect to a transition model having observable visible states and unobservable hidden states and expressing a transition from a present visible state to a subsequent visible state according to an action, the set of gain vectors being generated for each visible state and used for calculation of a cumulative expected gain at and after a reference point in time, the method comprising: setting, with respect to each hidden state, a probability distribution over the hidden states for selection used to select vectors to be included in the set of gain vectors from the gain vectors including a component for a cumulative gain; and selection by including, in the set of gain vectors, with priority, the gain vector giving the maximum of the cumulative expected gain with respect to the probability distribution for selection.