2010/04/22 by Markus N. Rabe, Sven Schewe, Rabe, Markus +2
Computer Science · #F.1.1 #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Formal Methods in Verification #G.3 #Petri Nets in System Modeling #Real-Time Systems Scheduling #Reinforcement Learning in Robotics #cs.FL
paper · pdf · doi:10.48550/arxiv.1004.4005
openalex publication_date 2010/04/22 · arxiv created 2010/06/04 · arxiv updated 2010/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish the existence of optimal scheduling strategies for time-bounded reachability in continuous-time Markov decision processes, and of co-optimal strategies for continuous-time Markov games. Furthermore, we show that optimal control does not only exist, but has a surprisingly simple structure: The optimal schedulers from our proofs are deterministic and timed-positional, and the bounded time can be divided into a finite number of intervals, in which the optimal strategies are positional. That is, we demonstrate the existence of finite optimal control. Finally, we show that these pleasant properties of Markov decision processes extend to the more general class of continuous-time Markov games, and that both early and late schedulers show this behaviour.