A Correctness Result for Synthesizing Plans With Loops in Stochastic Domains
This work addresses a fundamental gap in robotics, video games, and logistics by enabling reliable plan synthesis in uncertain environments, though it appears incremental as it builds on existing deterministic techniques.
The paper tackles the problem of synthesizing finite-state controllers (FSCs) with loops in stochastic domains, presenting new theoretical results that provide correctness guarantees for termination and goal satisfaction.
Finite-state controllers (FSCs), such as plans with loops, are powerful and compact representations of action selection widely used in robotics, video games and logistics. There has been steady progress on synthesizing FSCs in deterministic environments, but the algorithmic machinery needed for lifting such techniques to stochastic environments is not yet fully understood. While the derivation of FSCs has received some attention in the context of discounted expected reward measures, they are often solved approximately and/or without correctness guarantees. In essence, that makes it difficult to analyze fundamental concerns such as: do all paths terminate, and do the majority of paths reach a goal state? In this paper, we present new theoretical results on a generic technique for synthesizing FSCs in stochastic environments, allowing for highly granular specifications on termination and goal satisfaction.