CaMeL: Learning Method Preconditions for HTN Planning

A great challenge in using any planning system to solve real-world problems is the difficulty of acquiring the domain knowledge that the system will need. We present a way to address part of this problem, in the context of Hierarchical Task Network (HTN) planning, by having the planning system learn the HTN methods incrementally under supervision of an expert. We present a general formal framework for learning HTN methods, and a supervised learning algorithm, named CaMeL, based on this formalism. We present theoretical results about CaMeL’s soundness, completeness, and convergence properties. We also report experimental results about its speed of convergence under different conditions. The experimental results suggest that CaMeL has the potential to be useful in real-world applications. Introduction A great challenge in using any planning system to solve real-world problems is the difficulty of acquiring the domain knowledge and the associated control rules (i.e., rules that help the planner to search the search space efficiently) that abstract the real-world domain. One way to address this issue is to design the planning system to learn the constituents of the planning domain and the associated control rules. This requires the system to be supervised by a domain expert who solves instances of the problems in that domain. This will result in a supervised learning process. In this paper, we discuss a supervised incremental learning algorithm in a Hierarchical Task Network (HTN) planning context. In recent years, several researchers have reported work on the HTN planning formalism and its applications (Wilkins 1990; Currie & Tate 1991; Erol, Hendler, & Nau 1994). The hierarchical semantics of this kind of planning gives us the ability to model planning problems in domains that are naturally hierarchical. A good example is planning in military environments, where conventional linear STRIPS-style planners (Fikes & Nilsson 1971) cannot be exploited to abstract the planning problems accurately. An example of using HTN planning in such environments is a system called HICAP (Muñoz-Avila et al. 1999), which has been used to assist with the authoring of plans for noncombatant evacuation operations. To support plan authoring, HICAP integrates the SHOP hierarchical planner (Nau et al. 1999) together with a case-based reasoning (CBR) system named NaCoDAE (Aha & Breslow 1997). As with any incremental learning problem, there are at least two approaches that one might consider for learning HTN methods. First, a lazy CBR approach can be used to directly replay plans previously generated by the human expert. It assumes that plans that were successfully used in situations similar to the current situation are likely to work now. Second, an eager approach can be used to induce methods that could be used to mimic the human expert. In either approach, adding new training samples, which represent human expert activities while solving an HTN planning problem, is expected to yield better approximations of the domain. However, due to the complexity of the semantics of HTN planning, one should carefully define the inputs and outputs of the learning algorithm and what learning means in this context. In this paper, we use an eager approach. In this paper, we introduce a theoretical basis for formally defining algorithms that learn preconditions for HTN methods. This formalism models situations when we have the following: General information about possible decompositions of tasks into subtasks, but without sufficient details to tell where each decomposition will be successful and when it won’t. Plan traces that are known to be successful or unsuccessful for certain problem instances. Such situations occur in several important practical domains, such as the domain of Noncombatant Evacuation Operations(DoD 1994; Lamber 1992), in which a military doctrine provides the planner with general information about how to carry out an evacuation operation, while the details of such an operation are not specified. We also discuss CaMeL (Candidate Elimination Method Learner), an algorithm that instantiates this formalism. We state theorems about CaMeL’s soundness, completeness, and convergence properties. Our experimental results show the speed with which CaMeL converges in different situations and suggest that CaMeL has the potential for use in deployed systems. Hierarchical Task Network Planning In an HTN planning system, instead of having traditional STRIPS-style operators with delete and add lists used to achieve goal predicates (Fikes & Nilsson 1971), the main goal of planning is to accomplish a list of given tasks. Each task can be decomposed into several subtasks using predefined methods. Each possible decomposition represents a new branch in the search space of the problem. At the bottom level of this hierarchy lie primitive tasks, whose actions can be executed using an atomic operator. In summary, the plan still consists of a list of instantiations of operators, partially ordered in some planners and fully ordered in other ones, but the correctness definition of the plan differs. In traditional planning, a plan is correct if it is executable, and the goal state is a subset of the world state after the plan’s execution (i.e., each goal atom is achieved by some operator in the plan). In HTN planning, a plan is correct if it is executable in the initial state of the world, and it achieves the task list that is given as an input in the planning problem using the methods defined as a part of planning domain. In other words, the main focus of an HTN planner is task decomposition, while a traditional planner focuses on achieving the desired state. In this paper we use a form of HTN planning called Ordered Task Decomposition (Nau et al. 1999) in which at each point in the planning process, the planner has a totally ordered list of tasks to accomplish. An HTN domain is a triple where: is a list of tasks. Each task has a name and zero or more arguments, each of which is either a variable symbol1 or a constant symbol. Each task can be either primitive or nonprimitive. A primitive task represents a concrete action, while a non-primitive task must be decomposed into simpler subtasks. is a collection of methods, each of which is a triple , where is a non-primitive task, is a totally-ordered list of tasks called a decomposition of , and (the set of preconditions) is a boolean formula of first-order predicate calculus. Every free variable in must appear in the argument list of , and every variable in must appear either in the argument list of or somewhere in . We will assume that each method can be uniquely identified by its first two parts, and (i.e., there will be no two different methods and such that ! ). is a collection of operators, each of which is a triple