Online learning algorithms continually update their models as data arrive, making it essential to accurately estimate the expected loss at the current time step. The prequential method is an effective estimation approach which can be practically deployed in various ways. However, theoretical guarantees have previously been established under strong conditions on the algorithm, and practical algorithms have hyperparameters which require careful tuning. We introduce OEUVRE, an estimator that evaluates each incoming sample on the function learned at the current and previous time steps, recursively updating the loss estimate in constant time and memory. We use algorithmic stability, a property satisfied by many popular online learners, for optimal updates and prove consistency, convergence rates, and concentration bounds for our estimator. We design a method to adaptively tune OEUVRE's hyperparameters and test it across diverse online and stochastic tasks. We observe that OEUVRE matches or outperforms other estimators even when their hyperparameters are tuned with oracle access to ground truth.

翻译：在线学习算法随着数据的到达持续更新其模型，因此准确估计当前时间步的期望损失至关重要。序贯预测方法是一种有效的估计方法，可通过多种方式实际部署。然而，先前理论保证仅在算法的强条件下建立，且实际算法包含需要仔细调优的超参数。我们提出OEUVRE估计器，该估计器基于当前及先前时间步学习到的函数评估每个输入样本，并以恒定时间和内存递归更新损失估计。我们利用算法稳定性——一种被许多流行在线学习器满足的性质——进行最优更新，并证明了估计器的一致性、收敛速率及集中界。我们设计了一种自适应调优OEUVRE超参数的方法，并在多种在线及随机任务中进行了测试。实验表明，即使其他估计器通过真实值先知调优超参数，OEUVRE仍能与之持平或表现更优。