  We propose a method for efficient training of Q-functions for
continuous-state Markov Decision Processes (MDPs) such that the traces of the
resulting policies satisfy a given Linear Temporal Logic (LTL) property. LTL, a
modal logic, can express a wide range of time-dependent logical properties
(including "safety") that are quite similar to patterns in natural language. We
convert the LTL property into a limit deterministic Buchi automaton and
construct an on-the-fly synchronised product MDP. The control policy is then
synthesised by defining an adaptive reward function and by applying a modified
neural fitted Q-iteration algorithm to the synchronised structure, assuming
that no prior knowledge is available from the original MDP. The proposed method
is evaluated in a numerical study to test the quality of the generated control
policy and is compared with conventional methods for policy synthesis such as
MDP abstraction (Voronoi quantizer) and approximate dynamic programming (fitted
value iteration).
