Subset-Saturated Cost Partitioning for Optimal Classical Planning

Cost partitioning is a method for admissibly adding multiple heuristics for state-space search. Saturated cost partitioning considers the given heuristics in sequence, assigning to each heuristic the minimum fraction of remaining costs that it needs to preserve its estimates for all states. We generalize saturated cost partitioning by allowing to preserve the heuristic values of only a subset of states and show that this often leads to stronger heuristics

Online Saturated Cost Partitioning for Classical Planning

Saturated cost partitioning is a general method for admissiblyadding heuristic estimates for optimal state-space search. Thealgorithm strongly depends on the order in which it considers the heuristics. The strongest previous approach precomputes a set of diverse orders and the corresponding saturatedcost partitionings before the search. This makes evaluatingthe overall heuristic very fast, but requires a long precomputation phase. By diversifying the set of orders online duringthe search we drastically speed up the planning process andeven solve slightly more tasks

Narrowing the Gap Between Saturated and Optimal Cost Partitioning for Classical Planning

In classical planning, cost partitioning is a method for admissibly combining a set of heuristic estimators by distributing operator costs among the heuristics. An optimal cost partitioning is often prohibitively expensive to compute. Saturated cost partitioning is an alternative that is much faster to compute and has been shown to offer high-quality heuristic guidance on Cartesian abstractions. However, its greedy nature makes it highly susceptible to the order in which the heuristics are considered. We show that searching in the space of orders leads to significantly better heuristic estimates than with previously considered orders. Moreover, using multiple orders leads to a heuristic that is significantly better informed than any single-order heuristic. In experiments with Cartesian abstractions, the resulting heuristic approximates the optimal cost partitioning very closely

State-dependent Cost Partitionings for Cartesian Abstractions in Classical Planning

Abstraction heuristics are a popular method to guide optimal search algorithms in classical planning. Cost partitionings allow to sum heuristic estimates admissibly by distributing action costs among the heuristics. We introduce state-dependent cost partitionings which take context information of actions into account, and show that an optimal state-dependent cost partitioning dominates its state-independent counterpart. We demonstrate the potential of our idea with a state-dependent variant of the recently proposed saturated cost partitioning, and show that it has the potential to improve not only over its state-independent counterpart, but even over the optimal state-independent cost partitioning. Our empirical results give evidence that ignoring the context of actions in the computation of a cost partitioning leads to a significant loss of information

Saturated Post-hoc Optimization for Classical Planning

Saturated cost partitioning and post-hoc optimization are two powerful cost partitioning algorithms for optimal classical planning. The main idea of saturated cost partitioning is to give each considered heuristic only the fraction of remaining operator costs that it needs to prove its estimates. We show how to apply this idea to post-hoc optimization and obtain a heuristic that dominates the original both in theory and on the IPC benchmarks

Additive Pattern Databases for Decoupled Search

Abstraction heuristics are the state of the art in optimal classical planning as heuristic search. Despite their success for explicit-state search, though, abstraction heuristics are not available for decoupled state-space search, an orthogonal reduction technique that can lead to exponential savings by decomposing planning tasks. In this paper, we show how to compute pattern database (PDB) heuristics for decoupled states. The main challenge lies in how to additively employ multiple patterns, which is crucial for strong search guidance of the heuristics. We show that in the general case, for arbitrary collections of PDBs, computing the heuristic for a decoupled state is exponential in the number of leaf components of decoupled search. We derive several variants of decoupled PDB heuristics that allow to additively combine PDBs avoiding this blow-up and evaluate them empirically

Cost Partitioning Heuristics for Stochastic Shortest Path Problems

In classical planning, cost partitioning is a powerful method which allows to combine multiple admissible heuristics while retaining an admissible bound. In this paper, we extend the theory of cost partitioning to probabilistic planning by generalizing from deterministic transition systems to stochastic shortest path problems (SSPs). We show that fundamental results related to cost partitioning still hold in our extended theory. We also investigate how to optimally partition costs for a large class of abstraction heuristics for SSPs. Lastly, we analyze occupation measure heuristics for SSPs as well as the theory of approximate linear programming for reward-oriented Markov decision processes. All of these fit our framework and can be seen as cost-partitioned heuristics

Counterexample-guided cartesian abstraction refinement and saturated cost partitioning for optimal classical planning

Heuristic search with an admissible heuristic is one of the most prominent approaches to solving classical planning tasks optimally. In the first part of this thesis, we introduce a new family of admissible heuristics for classical planning, based on Cartesian abstractions, which we derive by counterexample-guided abstraction refinement. Since one abstraction usually is not informative enough for challenging planning tasks, we present several ways of creating diverse abstractions. To combine them admissibly, we introduce a new cost partitioning algorithm, which we call saturated cost partitioning. It considers the heuristics sequentially and uses the minimum amount of costs that preserves all heuristic estimates for the current heuristic before passing the remaining costs to subsequent heuristics until all heuristics have been served this way. In the second part, we show that saturated cost partitioning is strongly influenced by the order in which it considers the heuristics. To find good orders, we present a greedy algorithm for creating an initial order and a hill-climbing search for optimizing a given order. Both algorithms make the resulting heuristics significantly more accurate. However, we obtain the strongest heuristics by maximizing over saturated cost partitioning heuristics computed for multiple orders, especially if we actively search for diverse orders. The third part provides a theoretical and experimental comparison of saturated cost partitioning and other cost partitioning algorithms. Theoretically, we show that saturated cost partitioning dominates greedy zero-one cost partitioning. The difference between the two algorithms is that saturated cost partitioning opportunistically reuses unconsumed costs for subsequent heuristics. By applying this idea to uniform cost partitioning we obtain an opportunistic variant that dominates the original. We also prove that the maximum over suitable greedy zero-one cost partitioning heuristics dominates the canonical heuristic and show several non-dominance results for cost partitioning algorithms. The experimental analysis shows that saturated cost partitioning is the cost partitioning algorithm of choice in all evaluated settings and it even outperforms the previous state of the art in optimal classical planning