Nested Value Iteration for Partially Satisfiable Co-Safe LTL Specifications (Extended Abstract)

We describe our recent work on cost-optimal policy generation, for co-safe linear temporal logic (LTL) specifications that are not satisfiable with probability one in a Markov decision process (MDP) model. We provide an overview of the approach to pose the problem as the optimisation of three standard objectives in a trimmed product MDP. Furthermore, we introduce a new approach for optimising the three objectives, in a decreasing order of priority, based on a “nested” value iteration, where one value table is kept for each objective.