A Theory of Goal-Oriented MDPs with Dead Ends
This addresses a foundational gap in probabilistic planning for AI, enabling modeling of scenarios with catastrophic events like airplane crashes, though it is incremental as it extends existing SSP frameworks.
The paper tackles the limitation of Stochastic Shortest Path MDPs, which assume no dead-end states, by proposing three new MDP classes that allow dead ends under weaker assumptions, and presents algorithms for optimal solving with a preliminary empirical study.
Stochastic Shortest Path (SSP) MDPs is a problem class widely studied in AI, especially in probabilistic planning. They describe a wide range of scenarios but make the restrictive assumption that the goal is reachable from any state, i.e., that dead-end states do not exist. Because of this, SSPs are unable to model various scenarios that may have catastrophic events (e.g., an airplane possibly crashing if it flies into a storm). Even though MDP algorithms have been used for solving problems with dead ends, a principled theory of SSP extensions that would allow dead ends, including theoretically sound algorithms for solving such MDPs, has been lacking. In this paper, we propose three new MDP classes that admit dead ends under increasingly weaker assumptions. We present Value Iteration-based as well as the more efficient heuristic search algorithms for optimally solving each class, and explore theoretical relationships between these classes. We also conduct a preliminary empirical study comparing the performance of our algorithms on different MDP classes, especially on scenarios with unavoidable dead ends.