Rigorously establishing the safety of black-box machine learning models concerning critical risk measures is important for providing guarantees about model behavior. Recently, Bates et. al. (JACM '24) introduced the notion of a risk controlling prediction set (RCPS) for producing prediction sets that are statistically guaranteed low risk from machine learning models. Our method extends this notion to the sequential setting, where we provide guarantees even when the data is collected adaptively, and ensures that the risk guarantee is anytime-valid, i.e., simultaneously holds at all time steps. Further, we propose a framework for constructing RCPSes for active labeling, i.e., allowing one to use a labeling policy that chooses whether to query the true label for each received data point and ensures that the expected proportion of data points whose labels are queried are below a predetermined label budget. We also describe how to use predictors (i.e., the machine learning model for which we provide risk control guarantees) to further improve the utility of our RCPSes by estimating the expected risk conditioned on the covariates. We characterize the optimal choices of label policy and predictor under a fixed label budget and show a regret result that relates the estimation error of the optimal labeling policy and predictor to the wealth process that underlies our RCPSes. Lastly, we present practical ways of formulating label policies and empirically show that our label policies use fewer labels to reach higher utility than naive baseline labeling strategies (e.g., labeling all points, randomly labeling points) on both simulations and real data.

翻译：严格确立黑盒机器学习模型在关键风险度量方面的安全性，对于提供模型行为保证至关重要。最近，Bates等人（JACM '24）提出了风险控制预测集（RCPS）的概念，用于从机器学习模型生成统计上保证低风险的预测集。我们的方法将这一概念扩展到序列设置中，即使在数据被自适应收集的情况下也能提供保证，并确保风险保证是任意时间有效的，即同时适用于所有时间步。此外，我们提出了一个用于主动标注构建RCPS的框架，即允许使用一种标注策略来选择是否查询每个接收数据点的真实标签，并确保查询标签的数据点预期比例低于预定的标注预算。我们还描述了如何利用预测器（即我们为其提供风险控制保证的机器学习模型），通过估计以协变量为条件的预期风险，进一步提高RCPS的效用。我们刻画了在固定标注预算下最优的标注策略和预测器选择，并展示了一个遗憾结果，该结果将最优标注策略和预测器的估计误差与我们RCPS所基于的财富过程联系起来。最后，我们提出了制定标注策略的实用方法，并通过仿真和真实数据实证表明，相较于朴素基线标注策略（例如标注所有点、随机标注点），我们的标注策略使用更少的标签即可达到更高的效用。