Verification of general Markov decision processes by approximate similarity relations and policy refinement
For researchers working on verification and control of complex stochastic systems, this work provides a theoretical framework for approximate reasoning with a trade-off between state distribution deviations and output distances.
The paper introduces new approximate similarity relations for general Markov decision processes with uncountable state spaces and metric outputs, enabling policy synthesis and control refinement from abstract models.
In this work we introduce new approximate similarity relations that are shown to be key for policy (or control) synthesis over general Markov decision processes. The models of interest are discrete-time Markov decision processes, endowed with uncountably-infinite state spaces and metric output (or observation) spaces. The new relations, underpinned by the use of metrics, allow in particular for a useful trade-off between deviations over probability distributions on states, and distances between model outputs. We show that the new probabilistic similarity relations, inspired by a notion of simulation developed for finite-state models, can be effectively employed over general Markov decision processes for verification purposes, and specifically for control refinement from abstract models.