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

arXiv: https://arxiv.org/abs/2605.06741 · HTML: https://mlsanity.com/paper/2605.06741/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 12 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 7 of 7)

- [Optimal Linear Decay Learning Rate Schedules and Further Refinements](https://mlsanity.com/paper/2310.07831/) (2023)
- [Adaptive Inertia: Disentangling the Effects of Adaptive Learning Rate and Momentum](https://mlsanity.com/paper/2006.15815/) (2020)
- [Layer-Specific Adaptive Learning Rates for Deep Networks](https://mlsanity.com/paper/1510.04609/) (2015)
- [Beyond Convexity -- Contraction and Global Convergence of Gradient Descent](https://mlsanity.com/paper/1806.06655/) (2018)
- [Conformal Mirror Descent with Logarithmic Divergences](https://mlsanity.com/paper/2209.02938/) (2022)
- [A note on the optimal convergence rate of descent methods with fixed step sizes for smooth strongly convex functions](https://mlsanity.com/paper/2106.08020/) (2021)
- [Convergence Rate Bounds for the Mirror Descent Method: IQCs, Popov Criterion and Bregman Divergence](https://mlsanity.com/paper/2304.03886/) (2023)

## Abstract (arXiv)

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.