Challenges in Finding Generalized Plans

We present a simple and precise definition of generalized planning together with five natural dimensions of quality for measuring any generalized plan. We argue that no existing approach excels in all these dimensions. In the remainder of the paper we present a new approach to generalized planning that addresses all five of these dimensions. The Problem of Generalized Planning Over the years, many researchers have addressed the problem of coming up with a ”general plan” that solves many different planning problems. Methods for doing so have included, among others, indexing and cataloging observed plans, annotating previously observed action sequences for future use, theorem proving, boolean satisfiability, etc. All of these approaches can be understood as developing generalized plans which “efficiently” map problem instances to “good” concrete, deterministic plans for solving them. This leads us to the following natural definition: Definition 1 A generalized plan is an algorithm, G, that maps problem instances, i, to a sequence of actions, s that solves i. We call the concrete plan s = G(i) the instantiation of the generalized plan, G, for instance i. A classical planner is the simplest form of a generalized plan. On the other hand, an algorithm, for instance the “Unstack” algorithm in blocks world for moving all blocks to the table, is a very specific generalized plan which produces output plans for the problem instances that it can solve much more easily than a classical planner: while(∃b(clear(b) ∧ ¬on-table(b)) : moveToTable(b) For this particular generalized plan, it is also very easy to test whether it can solve a given problem instance: the goal should be to have all blocks on the table. In finding generalized plans, any approach needs to address some common challenges: 1. Complexity of checking applicability 2. Complexity of plan instantiation 3. Quality of the instantiated plan