AI 中文总结
针对直线度量下带延迟的在线聚合问题，提出学习增强型、随机型及结合两者的算法，给出相关鲁棒性、一致性或竞争比指标，经数值实验验证性能。
AI 中文摘要
本文研究直线度量下带延迟的学习增强型与随机在线聚合问题，考虑以在线建议服务长度形式提供的指导信息，从鲁棒性与一致性两方面评估算法性能。对任意λ∈(0,1]，本文首先提出确定性学习增强算法\textsc{Balance}，其鲁棒性为(4/λ+1/λ²)、一致性为(4+λ)；还针对经典对抗模型提出该问题的随机算法，对无感知敌手的竞争比为(e+1)，优于确定性基准算法\textsc{Balance}的5竞争比，且该竞争比低于确定性在线算法的4下界。此外，本文给出随机在线算法竞争比的e下界，改进此前e/(e-1)的下界；结合两种思路得到随机学习增强算法，鲁棒性为(e/λ+1/λ²)、一致性为(e+λ)。最后通过数值实验补充理论分析，评估算法的经验性能。
英文摘要
This paper studies learning-augmented and randomized online aggregation with delays on a line metric. We consider advice given as online suggested service lengths, and evaluate the algorithms in terms of robustness and consistency. For each $λ\in (0,1]$, we first propose a deterministic learning-augmented \textsc{Balance} algorithm that is $(4/λ+1/λ^2)$-robust and $(4+λ)$-consistent. We also propose a randomized algorithm for the problem in the classical adversarial model, which is $(e+1)$-competitive against an oblivious adversary, improving over the deterministic $5$-competitive \textsc{Balance} benchmark~\cite{bienkowski2013chain}. Notably, this competitive ratio is even lower than the lower bound of $4$ for deterministic online algorithms. Moreover, we establish a lower bound of $e$ on the competitive ratio of randomized online algorithms, improving the previous lower bound of $e/(e-1)$. Besides, we combine the two ideas and obtain a randomized learning-augmented algorithm that is $(e/λ+1/λ^2)$-robust and $(e+λ)$-consistent. Finally, we conduct numerical experiments to complement our theoretical analysis and evaluate the empirical performance of our algorithms.
