A Closed-Form Upper Bound for Admissible Learning-Rate Steps in Belief-Space Dynamics

TL;DR

This paper derives a precise formula for the maximum admissible learning-rate step in belief-space updates, ensuring contractivity in KL/Bregman geometry, moving beyond heuristic tuning.

Contribution

It provides a closed-form upper bound for learning-rate steps in belief-space dynamics, grounded in geometric contractivity conditions.

Findings

Derived a formula for the upper bound of admissible steps

Ensured contractivity in KL/Bregman geometry for belief updates

Moved from heuristic to formula-based step size selection

Abstract

Learning-rate steps are usually treated as hyperparameters. This paper isolates a local beliefspace calculation: when an update is modeled as a projected forward step on the probability simplex, admissibility means contractivity in the natural KL/Bregman geometry. Under this model, the upper bound of an admissible step is not a tuning slogan but a formula.