# Latency and Ordering Effects in Online Decisions

arXiv: https://arxiv.org/abs/2511.13060 · HTML: https://mlsanity.com/paper/2511.13060/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 12 references that are in the map.
- First posted on arXiv 17 Nov 2025.

## Builds on (most cited first, 1 of 1)

- [Stochastic model-based minimization of weakly convex functions](https://mlsanity.com/paper/1803.06523/) (2018)

## Abstract (arXiv)

Online decision systems routinely operate under delayed feedback and order-sensitive (noncommutative) dynamics: actions affect which observations arrive, and in what sequence. Taking a Bregman divergence D_Phi as the loss benchmark, we prove that the excess benchmark loss admits a structured lower bound L ≥ Lideal + g1(λ) + g2(varepsilon_star) + g12(λ,varepsilon_star) - Dncx, where g1 and g2 are calibrated penalties for latency and order-sensitivity, g12 captures their geometric interaction, and Dncx≥ 0 is a nonconvexity/approximation penalty that vanishes under convex Legendre assumptions. We extend this inequality to prox-regular and weakly convex settings, obtaining robust guarantees beyond the convex case. We also give an operational recipe for estimating and monitoring the four terms via simple 2× 2 randomized experiments and streaming diagnostics (effective sample size, clipping rate, interaction heatmaps). The framework packages heterogeneous latency, noncommutativity, and implementation-gap effects into a single interpretable lower-bound statement that can be stress-tested and tuned in real-world systems.