发表机构
Huazhong University of Science and Technology（华中科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对度量任务系统，提出地标压缩值预测方法，仅预测少量地标值并通过Lipschitz扩展重建其余值，实现加性超额成本上界，并证明匹配下界及学习保证。
AI 中文摘要
度量任务系统（MTS）的学习增强算法可以利用规范对偶值的预测，但现有公式通常需要对每个状态进行预测。我们研究这些预测是否可以压缩到一小部分代表性状态，同时保留其算法价值。我们引入了地标压缩值预测，其中预测器仅报告$m$个地标处的预测对偶值，其余值通过Lipschitz扩展重建。我们的算法实现了加性超额成本$O(T\\,r(L) + \sum_t \delta_t)$，其中$r(L)$是地标的覆盖半径，$\delta_t$测量预测误差直至加性偏移；局部和值相关的界细化了这一保证。对于单位间隔有限线上的稀疏地标集，我们证明了每个使用固定地标的随机算法的匹配下界$\Omega(T r_m)$，即使预先访问其整个精确绝对值表也是如此。预测接口也很重要：在具有一个地标的两个状态上，精确绝对值允许与地平线无关的超额，而精确相对值迫使最坏情况下的预期超额与$T$线性相关。我们给出了学习压缩预测表的PAC保证，对于固定地标具有有效的经验风险最小化。我们的结果将度量覆盖、预测接口和在线MTS中压缩预测的学习保证联系起来。
英文摘要
Learning-augmented algorithms for metrical task systems (MTS) can exploit predictions of canonical dual values, but existing formulations typically require a prediction for every state. We study whether these predictions can be compressed to a small set of representative states while retaining their algorithmic value. We introduce landmark-compressed value predictions, in which the predictor reports predicted dual values only at $m$ landmarks and the remaining values are reconstructed by a Lipschitz extension. Our algorithm achieves additive excess cost $O(T\,r(L) + \sum_t δ_t)$, where $r(L)$ is the covering radius of the landmarks and $δ_t$ measures prediction error up to additive shifts; local and value-dependent bounds refine this guarantee. For sparse landmark sets on unit-spaced finite lines, we prove a matching $Ω(T r_m)$ lower bound for every randomized algorithm using fixed landmarks, even with advance access to their entire exact absolute-value table. The prediction interface also matters: on two states with one landmark, exact absolute values permit horizon-independent excess, whereas exact relative values force worst-case expected excess linear in $T$. We give PAC guarantees for learning compressed prediction tables, with efficient empirical-risk minimization for fixed landmarks. Our results connect metric coverage, prediction interfaces, and learning guarantees for compressed predictions in online MTS.
Comments33 pages
