On the Computational Complexity of Stackelberg Planning and Meta-Operator Verification

Published: 12 Feb 2024, Last Modified: 06 Mar 2024ICAPS 2024EveryoneRevisionsBibTeXCC BY 4.0
Keywords: Computational Complexity, Stackelberg Planning, Meta-Operator Verification
Abstract: Stackelberg planning is a two-player variant of classical planning, in which one player tries to ``sabotage'' the other player in achieving its goal. This yields a bi-objective planning problem, which appears to be computationally more challenging than the single-player case. But is this actually true? All investigations so far focused on practical aspects, i.e., algorithms, and applications like cyber-security or very recently for meta-operator verification in classical planning. We close this gap by conducting the first theoretical complexity analysis of Stackelberg planning. We show that in general Stackelberg planning is no harder than classical planning. Under a polynomial plan-length restriction, however, Stackelberg planning is a level higher up in the polynomial complexity hierarchy, suggesting that compilations into classical planning come with an exponential plan-length increase. In attempts to identify tractable fragments exploitable, e.g., for Stackelberg planning heuristic design, we further study its complexity under various planning task restrictions, showing that Stackelberg planning remains intractable where classical planning is not. We finally inspect the complexity of the meta-operator verification, which in particular gives rise to a new interpretation as the dual problem of Stackelberg plan existence.
Primary Keywords: Theory
Category: Short
Student: No
Supplemtary Material: pdf
Submission Number: 143