Latency and Ordering Effects in Online Decisions

• URL: http://arxiv.org/abs/2511.13060v1
• Date: Mon, 17 Nov 2025 07:08:05 GMT
• Title: Latency and Ordering Effects in Online Decisions
• Authors: Duo Yi,
• Abstract summary: Online decision systems operate under delayed feedback and order-sensitive dynamics.<n>We package heterogeneous latency, noncommutativity, and implementation-gap effects into a single lower-bound statement.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $D_Φ$ as the loss benchmark, we prove that the excess benchmark loss admits a structured lower bound $L \ge L_{\mathrm{ideal}} + g_1(λ) + g_2(\varepsilon_\star) + g_{12}(λ,\varepsilon_\star) - D_{\mathrm{ncx}}$, where $g_1$ and $g_2$ are calibrated penalties for latency and order-sensitivity, $g_{12}$ captures their geometric interaction, and $D_{\mathrm{ncx}}\ge 0$ 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 $2\times 2$ 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.

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