We propose and evaluate a system which learns a neural-network heuristic function for forward search-based, satisficing classical planning. Our system learns distance-to-goal estimators from scratch, given a single PDDL training instance. Training data is generated by backward regression search or by backward search from given or guessed goal states. In domains such as the 24-puzzle where all instances share the same search space, such heuristics can also be reused across all instances in the domain. We show that this relatively simple system can perform surprisingly well, sometimes competitive with well-known domain-independent heuristics.

Learning Search-Space Specific Heuristics Using Neural Network

Cost partitioning admissibly combines the information from multiple heuristics for state-space search. We use a greedy method called saturated cost partitioning that considers the heuristics in sequence and assigns the minimal fraction of the remaining costs that it needs to preserve the heuristic estimates. In this work, we address the problem of using more expressive transition cost functions with saturated cost partitioning to obtain stronger heuristics. Our contribution is subset-saturated transition cost partitioning that combines the concepts of using transition cost functions and prioritizing states that look more important during the search. Our empirical evaluation shows that this approach still causes too much computational overhead but leads to more informed heuristics.


Subset-Saturated Transition Cost Partitioning for Optimal Classical Planning

Pattern database (PDB) is one of the most popular automated heuristic generation techniques. A PDB maps states in a planning task to abstract states by considering a subset of variables and stores their optimal costs to the abstract goal in a look up table. As the result of the progress made on symbolic search over recent years, symbolic-PDB-based planners achieved impressive results in the International Planning Competition (IPC) 2018. Among them, Complementary 1 (CPC1) tied as the second best planners and the best nonportfolio planners in the cost optimal track, only 2 tasks behind the winner. It uses a combination of different pattern generation algorithms to construct PDBs that are complementary to existing ones. As shown in the post contest experiments, there is room for improvement. In this paper, we would like to present our work on refining the PDB construction mechanism of CPC1. By testing on IPC 2018 benchmarks, the results show that a significant improvement is made on our modified planner over the original version.

Refinements on the Complementary PDB Construction Mechanism

We consider the bi-criteria shortest-path problem where we want to compute shortest paths on a graph that simultaneously balance two cost functions. While this problem has numerous applications, there is usually no path minimizing both cost functions simultaneously. 
Thus, we typically consider the set of paths where no path is strictly better then the others in both cost functions, a set called the Pareto-optimal frontier. Unfortunately, the size of this set may be exponential in the number of graph vertices and the general problem is \NP-hard. While existing schemes to approximate this set exist, they may be slower than exact approaches when applied to relatively small instances and running them on graphs with even a moderate number of nodes is often impractical. The crux of the problem lies in how to efficiently approximate the Pareto-optimal frontier. Our key insight is that the Pareto-optimal frontier can be approximated using \emph{pairs} of paths. This simple observation allows us to run a best-first-search while efficiently and effectively pruning away intermediate solutions in order to obtain an approximation of the Pareto frontier for any given approximation factor. We compared our approach with an adaptation of BOA*, the state-of-the-art algorithm for computing exact solutions to the bi-criteria shortest-path problem. Our experiments show that as the problem becomes harder, the speedup obtained becomes more pronounced. Specifically, on large roadmaps, we obtain an average speedup of more than $\times 8.5$ and a maximal speedup of over $\times 148$. 

Approximate bi-criteria search by efficient representation of subsets of the Pareto-optimal frontier

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

Online Saturated Cost Partitioning for Classical Planning

This paper investigates the use of lifted heuristics, inspired by the more classical ones for the resolution of STRIPS-like problems, for the efficient resolution of timeline-based planning problems. We propose, in particular, a new heuristic strategy which, while maintaining the variables lifted, allows more accurate decisions. Furthermore, the concepts presented in this work pave the way for a new type of heuristics which, at present, allow this kind of solvers a significant performance improvement.


Investigating Lifted Heuristics for Timeline-based Planning

There exists no planning algorithm that outperforms all others.
Therefore, it is important to know which algorithm works
well on a task. A recently published approach uses either image
 or graph convolutional neural networks to solve this problem 
and achieves top performance. Especially the transformation
from the task to an image ignores a lot of information.
Thus, we would like to know what the network is learning
and if this is reasonable. As this is currently not possible, we
take one step back. We identify a small set of simple graph
features and show that elementary and interpretable machine
learning techniques can use those features to outperform the
neural network based approach. Furthermore, we evaluate the
importance of those features and verify that the performance
of our approach is robust to changes in the training and test
data.

Simplified Planner Selection

In classical planning as heuristic search, duplicate state pruning is a standard method to avoid unnecessarily handling the same state multiple times. In decoupled search, similar to symbolic search approaches, search nodes, called decoupled states, do not correspond to individual states, but to entire sets of states. As a result, duplicate state pruning cannot be applied in a straightforward manner. Instead, dominance pruning is employed, taking into account the state sets. We observe that the time required for dominance checking dominates the overall runtime, and propose two ways of tackling this issue. Our main contribution (1) is a stronger variant of dominance checking for optimal planning, where efficiency and pruning power are most crucial. The new variant greatly improves the latter, without incurring a computational overhead. Furthermore, (2) we develop and implement three methods that make the dominance check more efficient: exact duplicate checking, which, albeit resulting in weaker pruning, can pay off due to the use of hashing; avoiding the dominance check when leaf state spaces are invertible; and exploiting the transitivity of the dominance relation to only check against the relevant subset of visited decoupled states. We show empirically that all our improvements are indeed beneficial across many standard benchmark domains.

An Analysis of Dominance Pruning in Decoupled Search

LM-cut is one of the most popular heuristics in optimal planning that computes strong admissible estimates of the perfect delete relaxation heuristic $h^+$. The heuristic iteratively computes disjunctive action landmarks for the current state, reducing their action costs until no more landmarks with remaining action costs can be found. These landmarks are generated by finding cuts in the justification graph, which depends on a precondition choice function mapping each action to its most expensive precondition according to $h^{max}$. This precondition is not necessarily unique, yet the performance of the heuristic heavily depends on this choice. We introduce and analyze several new tie breaking strategies for the precondition choice function, and evaluate their effectiveness on the IPC benchmarks. Furthermore, we suggest a modification to the computation of the cut, which trades a negligible loss in heuristic accuracy for a significant speedup of the LM-cut computation.

Beating LM-cut with LM-cut: Quick Cutting and Practical Tie Breaking for the Precondition Choice Function

Dealing with discrete and continuous changes in real-world dynamic environments is of great importance for robots. Despite the success of previous approaches, they impose severe restrictions, such as convex quadratic constraints on state variables, which limits the expressivity of the problem, especially when the problem is non-convex. In this paper, we propose a novel algorithm framework based on recurrent neural networks. We cast the mixed planning with discrete and continuous actions in non-convex domains as a gradient descent search problem. In the experiment, we exhibit that our algorithm framework is both effective and efficient, especially when solving non-convex planning problems.

RNNs Based Planning with Discrete and Continuous Actions

A well known result is that, given a consistent heuristic and no other source of information, A* does expand a minimal number of nodes up to tie-breaking. We extend this analysis for A* with dominance pruning, which exploits a dominance relation to eliminate some states during the search. We show that the expansion order of A* is not necessarily optimally efficient when considering dominance pruning with arbitrary dominance relations, but it remains optimally efficient under certain restrictions for the heuristic and dominance relation.


On the Optimal Efficiency of A* with Dominance Pruning

Stubborn sets are an optimality-preserving pruning technique for factored state-space search, for example in classical planning. Their applicability is limited by their computational overhead. We describe a new algorithm for computing stubborn sets that is based on the state variables of the state space, while previous algorithms are based on its actions. Typical factored state spaces tend to have far fewer state variables than actions, and therefore our new algorithm is much more efficient than the previous state of the art, making stubborn sets a viable technique in many cases where they previously were not.


An Atom-Centric Perspective on Stubborn Sets

The need for data in planning has long been established, by, e.g., machine learning based approaches. The existing data, however, is quite limited. There exists only a relatively small amount of hand-crafted planning domains, mostly introduced through International Planning Competitions. Further, this collection of domains is not necessarily diverse: many of these domains are some variants of the transportation problem.
In this work, we alleviate the shortage in existing planning tasks by automatically generating tasks of a particular causal structure. Given any graph G, we show how to create a SAS+ planning task with the causal graph isomorphic to G. We create a large collection of planning tasks by randomly generating graphs of various structural restrictions and creating planning tasks for these graphs, but also, more importantly, we provide the community with a tool that allows for on-demand generation of additional, possibly larger tasks. Our experimental evaluation ensures that the generated collection is interesting for the current state of affairs in classical cost-optimal planning, showing the performance of state-of-the-art symbolic search and heuristic search based planners.

Generating Data In Planning: SAS+ Planning Tasks of a Given Causal Structure

Diverse planning is an important problem in automated planning with various real world applications. Recently, diverse planning has seen renewed interest, with work that defines a taxonomy of computational problems with respect to both plan quality and solution diversity. However, despite the recent advances in diverse planning the variety of approaches and the number of available tools for these problems are still quite limited, even nonexistent for several computational problems. In this work, we aim to extend the portfolio of approaches and tools for various computational problems in diverse planning. To that end, we introduce a novel approach to finding solutions for three computational problems within diverse planning and present planners for these three problems. For one of these problems, our approach is the first one that is able to provide solutions to the problem. For another, we show that top-k and top quality planners can provide, albeit naive, solutions to the problem and we extend these planners to improve the diversity of the obtained solution. Finally, for the third problem, we show that some existing diverse planners provide solutions to the problem, as well as describe our suggested approach. We empirically show our suggested approach to compare favorably with these existing planners.

Bounding Quality in Diverse Planning

The benchmarks from previous International Planning Competitions are commonly used to evaluate new planning algorithms. Since this set has grown organically over the years, it has several flaws: it contains duplicate tasks, trivially solvable domains, unsolvable tasks and tasks with modelling errors. Also, different domain sizes complicate the aggregation of results. Most importantly, however, the range of task difficulty is very small in many domains. We propose an automated method for creating benchmarks that solves these issues. To find a good scaling in difficulty, we automatically configure the parameters of benchmarks domains. We show that the resulting benchmark set improves empirical comparisons by allowing to differentiate between planners more easily.

ICAPS 2020 Workshop HSDIP Submissions