This paper investigates an information update system in which a mobile device monitors a physical process and sends status updates to an access point (AP). A fundamental trade-off arises between the timeliness of the information maintained at the AP and the update cost incurred at the device. To address this trade-off, we propose an online algorithm that determines when to transmit updates using only available observations. The proposed algorithm asymptotically achieves the optimal competitive ratio against an adversary that can simultaneously manipulate multiple sources of uncertainty, including the operation duration, information staleness, update cost, and update opportunities. Furthermore, by incorporating machine learning (ML) advice of unknown reliability into the design, we develop an ML-augmented algorithm that asymptotically attains the optimal consistency-robustness trade-off, even when the adversary can additionally corrupt the ML advice. The optimal competitive ratio scales linearly with the range of update costs, but is unaffected by other sources of uncertainty. Moreover, an optimal competitive online algorithm exhibits a threshold-like response to the ML advice: it either fully trusts or completely ignores the ML advice, as partially trusting the advice cannot improve the consistency without severely degrading the robustness. Extensive simulations in stochastic settings further validate the theoretical findings in the adversarial environment.

翻译：本文研究一种信息更新系统，其中移动设备监控物理过程并向接入点（AP）发送状态更新。在AP所维护信息的及时性与设备产生的更新成本之间存在根本性的权衡。为解决这一权衡，我们提出一种仅利用可用观测值来决定何时传输更新的在线算法。所提算法渐近地实现了最优竞争比，其对抗的对手可同时操纵多个不确定性来源，包括操作时长、信息陈旧度、更新成本和更新机会。此外，通过将可靠性未知的机器学习（ML）建议纳入设计，我们开发了一种ML增强算法，即使对手还能破坏ML建议，该算法也能渐近达到最优的一致性-鲁棒性权衡。最优竞争比随更新成本的范围线性增长，但不受其他不确定性来源的影响。此外，一种最优竞争性在线算法对ML建议表现出阈值式响应：它要么完全信任ML建议，要么完全忽略ML建议，因为部分信任建议无法在不严重损害鲁棒性的情况下提升一致性。在随机设置下的大量仿真进一步验证了对抗环境中的理论发现。