Computational Approaches for Stochastic Shortest Path on Succinct MDPs
This work addresses computational challenges in AI planning and decision-making under uncertainty, but it appears incremental as it builds on existing MDP frameworks with new methods for bounds.
The paper tackles the stochastic shortest path problem for succinct Markov decision processes by presenting polynomial-time computational approaches for upper and lower bounds, applicable even to infinite-state MDPs, and demonstrates effectiveness through experimental results on classical AI examples.
We consider the stochastic shortest path (SSP) problem for succinct Markov decision processes (MDPs), where the MDP consists of a set of variables, and a set of nondeterministic rules that update the variables. First, we show that several examples from the AI literature can be modeled as succinct MDPs. Then we present computational approaches for upper and lower bounds for the SSP problem: (a)~for computing upper bounds, our method is polynomial-time in the implicit description of the MDP; (b)~for lower bounds, we present a polynomial-time (in the size of the implicit description) reduction to quadratic programming. Our approach is applicable even to infinite-state MDPs. Finally, we present experimental results to demonstrate the effectiveness of our approach on several classical examples from the AI literature.