A Theory of Goal-Oriented MDPs with Dead Ends

TL;DR

This paper extends the theory of Stochastic Shortest Path MDPs to include dead-end states, introducing new classes and algorithms for solving these more realistic and complex scenarios.

Contribution

It proposes three new MDP classes that incorporate dead ends, along with value iteration and heuristic algorithms for solving them, filling a theoretical gap in SSP modeling.

Findings

Algorithms successfully solve MDPs with dead ends.

Theoretical relationships between the new classes are established.

Preliminary empirical results show effectiveness on scenarios with dead ends.

Abstract

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.