Title: Robbins-Monro conditions for persistent exploration learning strategies,
Abstract: We formulate simple assumptions, implying the Robbins-Monro conditions for
the $Q$-learning algorithm with the local learning rate, depending on the
number of visits of a particular state-action pair (local clock) and the number
of iteration (global clock). It is assumed that the Markov decision process is
communicating and the learning policy ensures the persistent exploration. The
restrictions are imposed on the functional dependence of the learning rate on
the local and global clocks. The result partially confirms the conjecture of
Bradkte (1994).