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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2511.13060 |
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| _version_ | 1866915622252707840 |
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| author | Yi, Duo |
| author_facet | Yi, Duo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13060 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Latency and Ordering Effects in Online Decisions Yi, Duo Machine Learning Artificial Intelligence 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. |
| title | Latency and Ordering Effects in Online Decisions |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2511.13060 |