The proof technique separates two stability mechanisms: a global comparison argument based on order monotonicity and W_∞ contraction brings an arbitrarily initialized iterate into a local neighborhood, where linearization and martingale analysis apply.

The proof separates two stability mechanisms. A global comparison argument, based on the order monotonicity of reward cumulative distribution functions and the $W_\infty$ contraction of the distributional Bellman operator, brings an arbitrarily initialized iterate into a local neighborhood.

http://arxiv.org/abs/2608.27313v1