Periodic learning about a hidden state variable

In active learning models the value function is necessarily convex in the priors. Hence, in combination with a concave objective, the decision problem need not become concave so that nonregularity problems are inherent. This paper considers an objective that unambiguously implies a quasi-convex decision problem and highlights the effect of the inherent nonregularities on active learning. A trigger policy for learning is shown to be optimal: the minimum amount of learning is optimal until uncertainty surpasses a critical value. At this trigger point the maximum amount of learning is chosen, uncertainty falls temporarily, and the cycle then repeats itself.