A Depth-Balanced Approach to Decompositional Planning for Problems where Hierarchical Depth is Requested

Hybrid planning with task insertion for solving classical planning problems, or decompositional planning, combines partial-order causal link planning with hierarchical task networks, where steps in the plan may represent composite (i.e., compound) actions that are decomposable into sub-steps using hierarchical knowledge. We have designed a planning algorithm that responds to a request for maximizing the hierarchical depth of plans while minimizing the plan length. In some applications, plans that adhere to hierarchical constraints are preferred over other valid plans. One of the main obstacles of this challenge is to incentivize the planner to insert composite actions while avoiding excessive search on the depth attribute. We introduce plan scoring heuristics that avoid over-discounting and under-discounting depth using a novel way to measure plan depth. We evaluate these heuristics on test problems and demonstrate that we can generate deep, low-cost solutions to planning problems while avoiding excessive search. Hybrid planning is a plan-space planning paradigm that combines partial-order causal link reasoning (Weld 1994) with hierarchical knowledge (Erol, Hendler, and Nau 1994) in order to solve a hybrid planning problem (the refinement of an initial partial plan into a plan with no flaws). While there exist several variants of hybrid planning (e.g. Young, Pollack, and Moore 1994, Lee-Urban 2012, Bechon et al. 2014), all variants afford some representation of task hierarchies through two kinds of tasks (i.e. steps): primitive and composite. The former are similar to steps in partial-order causal link (POCL) planning. The latter are drawn from hierarchical task network (HTN) planning (but also contain preconditions and effects as in POCL planning); they represent abstract tasks involving several moreprimitive steps. Whereas a primitive step that has been added to a plan can be directly executed (assuming its preconditions hold), composite steps that have been added are not directly executable; a more primitive sub-plan for the composite step must be found that depends on the composite’s preconditions and that achieves the composite’s effects. Such a sub-plan may be input to a hybrid planner through a decomposition method. Our planning applications make a non-standard depth request for hybrid planners. The request is that the planner maximizes the ratio of hierarchical depth (number of decomposition methods) to plan length (number of primitive tasks) of generated plans. The number of decomposition methods it uses to refine the initial plan is an integral part of the planning problem’s solution. Composite tasks are not wholly substituted for sub-plans that decompose them, but rather kept around to identify the hierarchical structure inherent in the plan. The underlying assumption is that the high-level structure of the plan (identified through the decomposition methods) is implicitly meaningful or useful for the planning agent. For example, in planning-based natural language generation (Garoufi 2014), plans may be preferred if they follow recognizable discourse patterns, which may be computed from data-driven observations and operationalized as hierarchical knowledge. Another example is the case of planning-based narrative generation (Young et al. 2013), wherein plans may be preferred if they follow normative narrative structure, often analytically identified as containing hierarchical segments (Prince 2003; Bordwell, Thompson, and Smith 1997). Typically, hybrid planners will insert a composite task, rather than a primitive task, if the composite task is explicitly needed because it has some primary effect: an effect that none of the tasks in its decompositional refinement can establish on its own (Kambhampati, Mali, and Srivastava 1998). A primary effect can characterize something that is more than the sum of its parts; for example, an argument is made by refuting facts, establishing background, referring to evidence, and making a conclusion, but none of these items are sufficient on its own. In contrast, in the classic travel planning domain, a goal to be located at a destination is achieved by a primitive task of exiting a plane that is at said destination; thus, a composite task – e.g. travel-by-plane – is not inserted into a plan unless it is estimated to save the planner time and effort for repairing the same goal condition. Given that heuristics tend to underestimate effort saved, and composite tasks add more to the plan length than primitive tasks, a planner using a best-first search is going to evaluate a repair with a primitive task as cheaper than a plan that makes the same repair with a composite task. We address the problem of fulfilling the depth request in hybrid domains where composite tasks may not have primary effects. The decision point we focus on is which task to insert to repair open conditions, which (in POCL planning) are flaws in the plan generated when a step has unsatisfied (i.e. open) Proceedings of the 1st ICAPS Workshop on Hierarchical Planning