When is the Pareto cache efficient?

Establish whether the Pareto cache used in compositional value iteration is efficient in regimes where single reachability queries are expensive and the cache hit rate is high, and characterize these conditions precisely.

Background

The proposed Pareto cache aims to reuse multi-objective analysis results across components and weights to avoid repeated local value iterations. Empirically, its benefit appears to depend on the cost of reachability queries and cache hit rates.

A formal characterization of the regimes where caching is provably beneficial would guide algorithmic choices and parameter tuning.