Arnaud Lequen

Windy Phung, Dominik Drexler, Arnaud Lequen et al.

Learned heuristics have recently become a competitive alternative to traditional domain-independent heuristics for satisficing planning. Existing approaches, however, focus on improving search guidance rather than guaranteeing admissibility, which makes them unsuitable for optimal classical planning. We present the first method for learning domain-dependent heuristics that are admissible by design and thus preserve the optimality guarantees of A* search. Instead of learning a direct mapping from states to heuristic values, we learn to construct abstractions that induce admissible heuristics. We use an LLM-driven evolutionary program-synthesis framework to obtain, for each domain, a program that produces a pattern collection for any task in that domain, and we combine the resulting patterns admissibly via saturated cost partitioning. Empirically, the learned programs encode interpretable domain-specific insights, run with negligible overhead at test time and yield heuristics that match the coverage of state-of-the-art domain-independent baselines on several domains while evaluating each state substantially faster.

Arnaud Lequen

We consider the problem of synthesizing interpretable models that recognize the behaviour of an agent compared to other agents, on a whole set of similar planning tasks expressed in PDDL. Our approach consists in learning logical formulas, from a small set of examples that show how an agent solved small planning instances. These formulas are expressed in a version of First-Order Temporal Logic (FTL) tailored to our planning formalism. Such formulas are human-readable, serve as (partial) descriptions of an agent's policy, and generalize to unseen instances. We show that learning such formulas is computationally intractable, as it is an NP-hard problem. As such, we propose to learn these behaviour classifiers through a topology-guided compilation to MaxSAT, which allows us to generate a wide range of different formulas. Experiments show that interesting and accurate formulas can be learned in reasonable time.

Arnaud Lequen, Martin C. Cooper, Frédéric Maris

Determining whether two STRIPS planning instances are isomorphic is the simplest form of comparison between planning instances. It is also a particular case of the problem concerned with finding an isomorphism between a planning instance $P$ and a sub-instance of another instance $P_0$ . One application of such a mapping is to efficiently produce a compiled form containing all solutions to P from a compiled form containing all solutions to $P_0$. We also introduce the notion of embedding from an instance $P$ to another instance $P_0$, which allows us to deduce that $P_0$ has no solution-plan if $P$ is unsolvable. In this paper, we study the complexity of these problems. We show that the first is GI-complete, and can thus be solved, in theory, in quasi-polynomial time. While we prove the remaining problems to be NP-complete, we propose an algorithm to build an isomorphism, when possible. We report extensive experimental trials on benchmark problems which demonstrate conclusively that applying constraint propagation in preprocessing can greatly improve the efficiency of a SAT solver.