Certified Unsolvability for SAT Planning with Property Directed Reachability

While classical planning systems can usually detect if a task is unsolvable, only recent research introduced a way to verify such a claim. These methods have already been applied to a variety of explicit and symbolic search algorithms, but so far no planning technique based on SAT has been covered with them. We fill this gap by showing how property directed reachability can produce proofs while only minimally altering the framework by allowing to utilize certificates for unsolvable SAT queries within the proof. We additionally show that a variant of the algorithm that does not use SAT calls can produce proofs that fit into the existing framework without requiring any changes

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

Landmarks, Critical Paths and Abstractions: What\u27s the Difference Anyway?

Current heuristic estimators for classical domain-independent planning are usually based on one of four ideas: delete relaxation, abstraction, critical paths, and, most recently, landmarks. Previously, these different ideas for deriving heuristic functions were largely unconnected. In my talk, I will show that these heuristics are in fact very closely related. Moreover, I will introduce a new admissible heuristic called the landmark cut heuristic which exploits this relationship. In our experiments, the landmark cut heuristic provides better estimates than other current admissible planning heuristics, especially on large problem instances

Understanding the Search Behaviour of Greedy Best-First Search

A classical result in optimal search shows that A* with an admissible and consistent heuristic expands every state whose f-value is below the optimal solution cost and no state whose f-value is above the optimal solution cost. For satisficing search algorithms, a similarly clear understanding is currently lacking. We examine the search behaviour of greedy best-first search (gbfs) in order to make progress towards such an understanding. We introduce the concept of high-water mark benches, which separate the search space into areas that are searched by a gbfs algorithm in sequence. High-water mark benches allow us to exactly determine the set of states that are not expanded under any gbfs tie-breaking strategy. For the remaining states, we show that some are expanded by all gbfs searches, while others are expanded only if certain conditions are met

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

Reinforcement Learning for Planning Heuristics

Informed heuristics are essential for the success of heuristic search algorithms. But, it is difficult to develop a new heuris- tic which is informed on various tasks. Instead, we propose a framework that trains a neural network as heuristic for the tasks it is supposed to solve. We present two reinforcement learning approaches to learn heuristics for fixed state spaces and fixed goals. Our first approach uses approximate value iteration, our second ap- proach uses searches to generate training data. We show that in some domains our approaches outperform previous work, and we point out potentials for future improvements

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

A Comparison of Cost Partitioning Algorithms for Optimal Classical Planning

Cost partitioning is a general and principled approach for constructing additive admissible heuristics for state-space search. Cost partitioning approaches for optimal classical planning include optimal cost partitioning, uniform cost partitioning, zero-one cost partitioning, saturated cost partitioning, post-hoc optimization and the canonical heuristic for pattern databases. We compare these algorithms theoretically, showing that saturated cost partitioning dominates greedy zero-one cost partitioning. As a side effect of our analysis, we obtain a new cost partitioning algorithm dominating uniform cost partitioning. We also evaluate these algorithms experimentally on pattern databases, Cartesian abstractions and landmark heuristics, showing that saturated cost partitioning is usually the method of choice on the IPC benchmark suite

Abstraction Heuristics, Cost Partitioning and Network Flows

Cost partitioning is a well-known technique to make admissible heuristics for classical planning additive. The optimal cost partitioning of explicit-state abstraction heuristics can be computed in polynomial time with a linear program, but the size of the model is often prohibitive. We study this model from a dual perspective and develop several simplification rules to reduce its size. We use these rules to answer open questions about extensions of the state equation heuristic and their relation to cost partitioning