Tight Bounds for Hybrid Planning

Abstract

How can we plan efficiently in a large and complex environment when the time budget is limited? Given the original simulator of the environment, which may be computationally very demanding, we propose to learn online an approximate but much faster simulator that improves over time. To plan reliably and efficiently while the approximate simulator is learning, we develop a method that adaptively decides which simulator to use for every simulation, based on a statistic that measures the accuracy of the approximate simulator. This allows us to use the approximate simulator to replace the original simulator for faster simulations when it is accurate enough under the current context, thus trading off simulation speed and accuracy. Experimental results in two large domains show that when integrated with POMCP, our approach allows to plan with improving efficiency over time.

Hierarchical planning and reasoning about partially ordered plans—From theory to practice

“…We showed that these constraints do not change the formalism's expressiveness in terms of plan existence complexity (Bercher et al. 2016; Bercher, Lin, and Alford 2022).…”

“…One is referred to as hybrid planning (Kambhampati, Mali, and Srivastava 1998; Bercher et al. 2016; Bercher, Lin, and Alford 2022), which combines HTN planning with POCL planning. In a nutshell, compound tasks specify preconditions and effects, which are used to pose constraints on decompositions methods, which now may also contain causal links.…”

“…These constraints are used to make sure that methods "implement" the modeler's intent of the compound task. We showed that these constraints do not change the formalism's expressiveness in terms of plan existence complexity (Bercher et al 2016;Bercher, Lin, and Alford 2022).…”

On the Computational Complexity of Plan Verification, (Bounded) Plan-Optimality Verification, and Bounded Plan Existence

“…In contrast, the plan verification problem in HTN planning is more computationally expensive. Previous works have already shown that it is already NP-complete in the grounded setting (Behnke, Höller, and Biundo 2015;Bercher, Lin, and Alford 2022). Those investigations rely on the standard definition of solutions being task networks that possess some executable linearization, whereas we define such a linearization as the solution itself.…”

“…Automated planning is the task of finding a course of actions called a plan which achieves a certain goal. An immense effort has been devoted to studying the computational complexity of the plan existence problem in the context of both non-hierarchical (classical) planning (Erol, Nau, and Subrahmanian 1991;Bylander 1994;Helmert 2006; Bäckström and Jonsson 2011) and hierarchical planning (Erol, Hendler, and Nau 1996;Geier and Bercher 2011;Alford et al 2014;Alford, Bercher, and Aha 2015a,b;Bercher, Lin, and Alford 2022) which is to decide whether a planning problem has a solution. In contrast, the number of research endeavors on the complexity of deciding whether there exists a plan up to a certain length (the bounded plan existence problem) is relatively small which is a standard way to frame the problem of finding an optimal plan as a decision problem.…”