We investigate learning heuristics for domain-specific planning. Prior work framed learning a heuristic as an ordinary regression problem. However, in a greedy best-first search, the ordering of states induced by a heuristic is more indicative of the resulting planner's performance than mean squared error. Thus, we instead frame learning a heuristic as a learning to rank problem which we solve using a RankSVM formulation. Additionally, we introduce new methods for computing features that capture temporal interactions in an approximate plan. Our experiments on recent International Planning Competition problems show that the RankSVM learned heuristics outperform both the original heuristics and heuristics learned through ordinary regression.
The ignoring delete lists relaxation is of paramount importance for both satisficing and optimal planning. In earlier work (Hoffmann 2005), it was observed that the optimal relaxation heuristic h+ has amazing qualities in many classical planning benchmarks, in particular pertaining to the complete absence of local minima. The proofs of this are hand-made, raising the question whether such proofs can be lead automatically by domain analysis techniques. In contrast to earlier disappointing results (Hoffmann 2005) - the analysis method has exponential runtime and succeeds only in two extremely simple benchmark domains - we herein answer this question in the affirmative. We establish connections between causal graph structure and h+ topology. This results in low-order polynomial time analysis methods, implemented in a tool we call TorchLight. Of the 12 domains where the absence of local minima has been proved, TorchLight gives strong success guarantees in 8 domains. Empirically, its analysis exhibits strong performance in a further 2 of these domains, plus in 4 more domains where local minima may exist but are rare. In this way, TorchLight can distinguish "easy" domains from "hard" ones. By summarizing structural reasons for analysis failure, TorchLight also provides diagnostic output indicating domain aspects that may cause local minima. Suboptimal heuristic search algorithms such as greedy best-first search allow us to find solutions when constraints of either time, memory, or both prevent the application of optimal algorithms such as A*. Guidelines for building an effective heuristic for A* are well established in the literature, but we show that if those rules are applied for greedy best-first search, performance can actually degrade. Observing what went wrong for greedy best-first search leads us to a quantitative metric appropriate for greedy heuristics, called Goal Distance Rank Correlation (GDRC). We demonstrate that GDRC can be used to build effective heuristics for greedy best-first search automatically. Weighted A* is the most popular satisficing algorithm for heuristic search. Although there is no formal guarantee that increasing the weight on the heuristic cost-to-go estimate will decrease search time, it is commonly assumed that increasing the weight leads to faster searches, and that greedy search will provide the fastest search of all. As we show, however, in some domains, increasing the weight slows down the search. This has an important consequence on the scaling behavior of Weighted A*: increasing the weight ad infinitum will only speed up the search if greedy search is effective. We examine several plausible hypotheses as to why greedy search would sometimes expand more nodes than A* and show that each of the simple explanations has flaws. Our contribution is to show that greedy search is fast if and only if there is a strong correlation between h(n) and d∗(n), the true distance-to-go, or if the heuristic is extremely accurate. Between 1998 and 2004, the planning community has seen vast progress in terms of the sizes of benchmark examples that domain-independent planners can tackle successfully. The key technique behind this progress is the use of heuristic functions based on relaxing the planning task at hand, where the relaxation is to assume that all delete lists are empty. The unprecedented success of such methods, in many commonly used benchmark examples, calls for an understanding of what classes of domains these methods are well suited for. In the investigation at hand, we derive a formal background to such an understanding. We perform a case study covering a range of 30 commonly used STRIPS and ADL benchmark domains, including all examples used in the first four international planning competitions. We prove connections between domain structure and local search topology – heuristic cost surface properties – under an idealized version of the heuristic functions used in modern planners. The idealized heuristic function is called h + , and differs from the practically used functions in that it returns the length of an optimal relaxed plan, which is NP-hard to compute. We identify several key characteristics of the topology under h + , concerning the existence non-existence of unrecognized dead ends, as well as the existence non-existence of constant upper bounds on the difficulty of escaping local minima and benches. These distinctions divide the (set of all) planning domains into a taxonomy of classes of varying h + topology. As it turns out, many of the 30 investigated domains lie in classes with a relatively easy topology. Most particularly, 12 of the domains lie in classes where FF’s search algorithm, provided with h + , is a polynomial solving mechanism. We also present results relating h + to its approximation as implemented in FF. The behavior regarding dead ends is provably the same. We summarize the results of an empirical investigation showing that, in many domains, the topological qualities of h + are largely inherited by the approximation. The overall investigation gives a rare example of a successful analysis of the connections between typical-case problem structure, and search performance. The theoretical investigation also gives hints on how the topological phenomena might be automatically recognizable by domain analysis techniques. We outline some preliminary steps we made into that direction.