Solving Goal Hybrid Markov Decision Processes Using Numeric Classical Planners

We present the domain-independent HRFF algorithm, which solves goal-oriented HMDPs by incrementally aggregating plans generated by the Metric-FF planner into a policy defined over discrete and continuous state variables. HRFF takes into account non-monotonic state variables, and complex combinations of many discrete and continuous probability distributions. We introduce new data structures and algorithmic paradigms to deal with continuous state spaces: hybrid hierarchical hash tables, domain determinization based on dynamic domain sampling or on static computation of probability distributions' modes, optimization settings under Metric-FF based on plan probability and length. We compare with HAO* on the Rover domain and show that HRFF outperforms HAO* by many order of magnitudes in terms of computation time and memory usage. We also experiment challenging and combinatorial HMDP versions of benchmarks from numeric classical planning, with continuous dead-ends and non-monotonic continuous state variables.