We consider a node-monitor pair, where the node's state varies with time. The monitor needs to track the node's state at all times; however, there is a fixed cost for each state query. So the monitor may instead predict the state using time-series forecasting methods, including time-series foundation models (TSFMs), and query only when prediction uncertainty is high. Since query decisions influence prediction accuracy, determining when to query is nontrivial. A natural approach is a greedy policy that predicts when the expected prediction loss is below the query cost and queries otherwise. We analyze this policy in a Markovian setting, where the optimal (OPT) strategy is a state-dependent threshold policy minimizing the time-averaged sum of query cost and prediction losses. We show that, in general, the greedy policy is suboptimal and can have an unbounded competitive ratio, but under common conditions such as identically distributed transition probabilities, it performs close to OPT. For the case of unknown transition probabilities, we further propose a projected stochastic gradient descent (PSGD)-based learning variant of the greedy policy, which achieves a favorable predict-query tradeoff with improved computational efficiency compared to OPT.

翻译：我们考虑一个节点-监控器对，其中节点的状态随时间变化。监控器需要持续跟踪节点的状态；然而，每次状态查询都存在固定成本。因此，监控器可以转而使用时序预测方法（包括时序基础模型）来预测状态，仅在预测不确定性较高时才进行查询。由于查询决策会影响预测准确性，确定何时查询并非易事。一种自然的方法是采用贪婪策略：当预期预测损失低于查询成本时进行预测，否则进行查询。我们在马尔可夫设定下分析此策略，其中最优策略是一种状态依赖的阈值策略，旨在最小化查询成本与预测损失的时间平均和。我们证明，一般而言，贪婪策略是次优的，且可能具有无界的竞争比；但在常见条件下（如状态转移概率同分布），其性能接近最优策略。针对转移概率未知的情况，我们进一步提出了一种基于投影随机梯度下降的贪婪策略学习变体，与最优策略相比，该变体在预测-查询权衡中取得了良好效果，并提升了计算效率。