One-Counter Markov Decision Processes
| Authors | |
|---|---|
| Year of publication | 2010 |
| Type | Article in Proceedings |
| Conference | Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms |
| MU Faculty or unit | |
| Citation | |
| Web | Link to SODA 2010 electronic proceedings |
| Field | Informatics |
| Keywords | Markov decision proces; probability; one counter MDP; reachability; termination |
| Description | We study One-Counter Markov Decision Processes (OC-MDPs), which extend finite-state MDPs with an unbounded counter. The counter can be incremented, decremented, or not changed during each state transition. Basic objectives for OC-MDPs include ``termination'' (Does the OC-MDP reach counter 0?) and ``limit'' questions (Is the limsup value infinity?). We may ask what is the optimal probability of such objectives, or ask for the existence and synthesis of optimal strategies. We show that several quantitative and almost-sure limit problems can be answered in polynomial time, and that almost-sure termination problems (without selection of desired terminal states) can also be answered in polynomial time. On the other hand, we show that the almost-sure termination problem with selected terminal states is PSPACE-hard and we provide an exponential time algorithm for this problem. We also characterize classes of strategies that suffice for optimality in several of these settings. |
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