Heuristic search planning with multi-objective probabilistic LTL constraints

We present an algorithm for computing cost-optimal stochastic policies for Stochastic Shortest Path problems (SSPs) subject to multi-objective PLTL constraints, i.e., conjunctions of probabilistic LTL formulas. Established algorithms capable of solving this problem typically stem from the area of probabilistic verification, and struggle with the large state spaces and constraint types found in automated planning. Our approach differs in two crucial ways. Firstly it operates entirely on-the-fly, bypassing the expensive construction of Rabin automata for the formulas and their prohibitive prior synchronisation with the full state space of the SSP. Secondly, it extends recent heuristic search algorithms and admissible heuristics for cost-constrained SSPs, to enable pruning regions made infeasible by the PLTL constraints. We prove our algorithm correct and optimal, and demonstrate encouraging scalability results.