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

Gregor Behnke, Marcel Steinmetz

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

Submission Number: 143