Constructing confidence intervals that are simultaneously valid across a class of estimates is central to tasks such as multiple mean estimation, generalization guarantees, and adaptive experimental design. We frame this as an ``error estimation problem," where the goal is to determine a high-probability upper bound on the maximum error for a class of estimates. We propose an entirely data-driven approach that derives such bounds for both finite and infinite class settings, naturally adapting to a potentially unknown correlation structure of random errors. Notably, our method does not require class complexity as an input, overcoming a major limitation of existing approaches. We present our simple yet general solution and demonstrate applications to simultaneous confidence intervals, excess-risk control and optimizing exploration in contextual bandit algorithms.

翻译：构建在估计类别上同时有效的置信区间，对于多重均值估计、泛化保证和自适应实验设计等任务至关重要。我们将此问题框架化为“误差估计问题”，其目标是为估计类别的最大误差确定一个高概率上界。我们提出了一种完全数据驱动的方法，可为有限和无限类别设置推导此类界，并自然地适应随机误差潜在未知的相关结构。值得注意的是，我们的方法不需要以类别复杂度作为输入，从而克服了现有方法的一个主要局限。我们提出了这一简单而通用的解决方案，并展示了其在同步置信区间、过风险控制以及上下文老虎机算法中探索优化方面的应用。