Knowing When to Stop Matters: A Unified Algorithm for Online Conversion under Horizon Uncertainty
This addresses the problem of optimizing resource trading under uncertainty for applications like energy markets, though it is incremental in extending existing models to more practical constraints.
The paper tackles the online conversion problem of trading a resource under changing prices with horizon uncertainty, proposing a unified algorithm that achieves optimal competitive guarantees across known, partially known, and unknown horizons, and extends it to a learning-augmented version with adaptive performance based on predictions.
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.