超越峰值积压：容量受限延迟多臂老虎机优化中的条件能量与时间几何
Beyond Peak Backlog: Conditional Energy and Temporal Geometry in Capacity-Constrained Delayed Bandit Optimization
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中文总结 AI 辅助
针对仅能跟踪有限反馈项的延迟多臂老虎机优化问题，引入条件能量接口得到更优延迟复杂度界，发现总延迟摘要一致时仍存在时序对极小极大悔度的影响。
中文摘要 AI 辅助
当学习器仅能跟踪C个待处理反馈项且被丢弃的反馈会永久丢失时，合适的延迟复杂度是多少？现有该模型下的单点多臂老虎机凸优化保证给出的复杂度为√(Tσ_max)，其中σ_max是峰值积压，尽管无限制跟踪能得到更精确的、与总延迟d_tot相关的√d_tot依赖关系。我们引入一种调度器侧的条件能量接口，该接口将速率适配与单点扰动过滤分离，并处理由随机准入产生的相关重要性权重。在相同的半全知预言机和路径式硬容量约束下，这得到一个无需调参的学习器，其延迟项规模为O(√(E_C d_tot))，仅含显式重启因子E_C；公共常数因子峰值界可消除该因子，且d_tot仍保持未知。在强凸性条件下，同一接口产生时间代价H_A(d)=Σ_t σ_t/(A+t)。两个具有相同延迟多重集、d_tot、σ_max和容量的延迟向量，其极小极大悔度仍可存在多项式差异，表明即使总延迟摘要一致，曲率下的时序仍有影响。最后，一个连续硬族将跟踪容量转换为零阶查询预算，并给出互补的容量饥饿下界端点。上述上界要求C≥ln T+1，且不构成完整的容量极小极大表征。
英文摘要
What is the right delay complexity when a learner can track only $C$ pending feedback items and discarded feedback is permanently lost? Existing one-point bandit convex optimization guarantees in this model pay $\sqrt{Tσ_{\max}}$, where $σ_{\max}$ is the peak backlog, although unlimited tracking admits the sharper $\sqrt{d_{\mathrm{tot}}}$ dependence on total delay. We introduce a scheduler-side conditional-energy interface that separates rate adaptation from the one-point perturbation filtration and handles the dependent importance weights created by randomized admission. Under the same semi-clairvoyant oracle and pathwise hard-capacity contract, this yields an untuned learner whose delay term scales as $O(\sqrt{E_C d_{\mathrm{tot}}})$, with only an explicit restart factor $E_C$; a public constant-factor peak bound removes this factor while $d_{\mathrm{tot}}$ remains unknown. Under strong convexity, the same interface yields the temporal cost $H_A(d)=\sum_t σ_t/(A+t)$. Two delay vectors with identical delay multisets, $d_{\mathrm{tot}}$, $σ_{\max}$, and capacity can nevertheless have polynomially different minimax regret, showing that timing matters under curvature even when aggregate delay summaries agree. Finally, a continuous hard family converts tracking capacity into a zeroth-order query budget and gives a complementary capacity-starvation lower endpoint. The upper bounds require $C\ge \ln T+1$ and do not constitute a complete capacity minimax characterization.
发表机构
- Minzu University of China（中央民族大学）
- ZeeLin (Beijing) Technology Co., Ltd.（泽林（北京）科技有限公司）
- Tsinghua University（清华大学）
机构由 AI 辅助整理，请以论文原文为准。
