Variational formulas and KPZ scaling for PMDPs

Derive an explicit variational formulation for the uniform value of oriented PMDPs with positive linearly dependent actions and determine which PMDPs exhibit Kardar–Parisi–Zhang (KPZ) scaling.

Background

The paper relates oriented PMDPs to directed last-passage percolation and obtains formulas in settings with linearly independent actions or suitable constant-path-length properties. It notes that extending these connections to more general action sets may provide new information about PMDP values.

Two unresolved questions are posed: obtaining an explicit variational formula when actions are positively linearly dependent, and identifying the PMDPs whose fluctuations and transversal behavior belong to the KPZ universality class.

References

The following questions are of particular interest: Is it possible to derive an explicit variational formulation for the uniform value of oriented PMDPs with positive linearly dependent actions? Which PMDPs exhibit KPZ scaling?

— Percolation Markov Decision Processes  (2609.19905 - García et al., 17 Sep 2026) in Section 8, Perspectives, Point 5