Computational Approaches for Stochastic Shortest Path on Succinct MDPs

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

Hierarchical Decomposition and Analysis for Generalized Planning

This paper presents new methods for analyzing and evaluating generalized plans that can solve broad classes of related planning problems. Although synthesis and learning of generalized plans has been a longstanding goal in AI, it remains challenging due to fundamental gaps in methods for analyzing the scope and utility of a given generalized plan. This paper addresses these gaps by developing a new conceptual framework along with proof techniques and algorithmic processes for assessing termination and goal-reachability related properties of generalized plans. We build upon classic results from graph theory to decompose generalized plans into smaller components that are then used to derive hierarchical termination arguments. These methods can be used to determine the utility of a given generalized plan, as well as to guide the synthesis and learning processes for generalized plans. We present theoretical as well as empirical results illustrating the scope of this new approach. Our analysis shows that this approach significantly extends the class of generalized plans that can be assessed automatically, thereby reducing barriers in the synthesis and learning of reliable generalized plans.Comment: Accepted for publication at JAI