Lately, the model of (Decision) Stochastic Timed Automata (DSTA) has been proposed, to model those Cyber Physical Systems displaying dense time (physical part), discrete actions and discontinuities such as timeouts (cyber part). The state of the art results on controlling DSTAs are however not ideal: in the case of infinite horizon, optimal controllers do not exist, while for timed bounded behaviors, we do not know how to build such controllers, even ε-optimal ones. In this paper, we develop a theory of Reinforcement Planning in the setting of DSTAs, for discounted infinite horizon objectives. We show that optimal controllers do exist in general. Further, for DSTAs with 1 clock (which already generalize Continuous Time MDPs with e.g. timeouts), we provide an effective procedure to compute ε-optimal controllers. It is worth noting that we do not rely on the discretization of the time space, but consider symbolic representations instead. Evaluation on a DSTA shows that this method can be more efficient. Last, we show on a counterexample that this is the furthest this construction can go, as it cannot be extended to 2 or more clocks. 2012 ACM Subject Classification Theory of computation → Timed and hybrid models Keywords and phrases reinforcement planning, timed automata, planning Digital Object Identifier 10.4230/LIPIcs...