标题： 知道何时停止很重要：在时间范围不确定性下的在线转换统一算法 显示英文标题

标题： Knowing When to Stop Matters: A Unified Algorithm for Online Conversion under Horizon Uncertainty

摘要： 本文研究了在线转换问题，该问题涉及在动态变化的价格下依次交易可分割资源（例如，能源）以最大化利润。 在线转换中的一个关键挑战是在时间范围不确定性下进行决策，其中交易的持续时间要么已知，要么部分揭示，要么完全未知。 我们提出了一种统一的算法，在这些时间范围模型中实现了最优的竞争保证，并考虑了实际约束，如箱型约束，这些约束限制了每一步的最大允许交易量。 此外，我们将算法扩展为一种增强学习的版本，利用时间范围预测来自适应地平衡性能：当预测准确时实现接近最优的结果，而在预测不可靠时仍保持强大的保证。 这些结果推进了在各种程度的时间范围不确定性下对在线转换的理解，并提供了更实用的策略来应对现实世界中的约束。 显示英文摘要

摘要： This paper investigates the online conversion problem, which involves sequentially trading a divisible resource (e.g., energy) under dynamically changing prices to maximize profit. A key challenge in online conversion is managing decisions under horizon uncertainty, where the duration of trading is either known, revealed partway, or entirely unknown. We propose a unified algorithm that achieves optimal competitive guarantees across these horizon models, accounting for practical constraints such as box constraints, which limit the maximum allowable trade per step. Additionally, we extend the algorithm to a learning-augmented version, leveraging horizon predictions to adaptively balance performance: achieving near-optimal results when predictions are accurate while maintaining strong guarantees when predictions are unreliable. These results advance the understanding of online conversion under various degrees of horizon uncertainty and provide more practical strategies to address real world constraints.