[LPH15] Bruno Lacerda, David Parker and Nick Hawes. Optimal Policy Generation for Partially Satisfiable Co-Safe LTL Specifications. In Proc. 24th International Joint Conference on Artificial Intelligence (IJCAI'15), pages 1587-1593, IJCAI/AAAI. August 2015. [pdf] [bib] [Proposes techniques for synthesising optimal policies in MDPs, building on multi-objective probabilistic model checking and PRISM, and applies them to robot task planning.]
Abstract. We present a method to calculate cost-optimal policies for co-safe linear temporal logic task specifications over a Markov decision process model of a stochastic system. Our key contribution is to address scenarios in which the task may not be achievable with probability one. We formalise a task progression metric and then, using multi-objective probabilistic model checking, generate policies which are formally guaranteed to, in decreasing order of priority: maximise the probability of completing the task; maximise progress towards completion, if this is not possible; and minimise the expected time or cost required. We illustrate and evaluate our approach in a robot task planning scenario, where the task is to visit a set of rooms that may be inaccessible during execution.