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

2025-02-06

AI Summary

This paper studies the online sequential exchange of divisible resources (e.g., energy) under dynamically evolving prices, where transaction durations exhibit horizon uncertainty—fully unknown, partially known, or fully known. To address this, we propose the first unified online algorithm achieving theoretically optimal competitive ratios across all three horizon models. We further design a learning-augmented variant that adaptively incorporates imprecise duration predictions: it retains over 90% of the optimal theoretical revenue even under 30% prediction error, ensuring both near-optimality when predictions are accurate and robustness when they are not. Our approach integrates competitive analysis, sequential optimization under box constraints, and the prediction-augmented online algorithm framework. Theoretically, we establish tight, horizon-agnostic optimal competitive ratio guarantees. Empirically, our method significantly outperforms existing baselines across diverse settings.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Sustainability of Web economics
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

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.

Problem

• Online conversion with horizon uncertainty
• Optimal trading strategy under dynamic prices
• Learning-augmented algorithm for adaptive performance

Innovation

• Unified algorithm for horizon uncertainty
• Learning-augmented adaptive balance
• Optimal competitive guarantees