Wait-Less Offline Tuning and Re-solving for Online Decision Making

TL;DR

This paper introduces a 'wait-less' online decision-making algorithm that combines LP-based and first-order methods, achieving low regret with improved computational efficiency for large-scale online linear programming problems.

Contribution

The paper proposes a novel algorithm that periodically re-solves LP subproblems and runs a first-order method in parallel, balancing regret guarantees and computational efficiency.

Findings

Achieves $oxed{ ext{O}( ext{log}(T/f) + extsqrt{f})}$ regret bound.

Balances computational efficiency with regret guarantees.

Provides a practical approach for large-scale online decision problems.

Abstract

Online linear programming (OLP) has found broad applications in revenue management and resource allocation. State-of-the-art OLP algorithms achieve low regret by repeatedly solving linear programming (LP) subproblems that incorporate updated resource information. However, LP-based methods are computationally expensive and often inefficient for large-scale applications. In contrast, recent first-order OLP algorithms are more computationally efficient but typically suffer from worse regret guarantees. To address these shortcomings, we propose a new algorithm that combines the strengths of LP-based and first-order OLP methods. The algorithm re-solves the LP subproblems periodically at a predefined frequency $f$ and uses the latest dual prices to guide online decision-making. In addition, a first-order method runs in parallel during each interval between LP re-solves, smoothing resource consumption. Our algorithm achieves $\mathscr{O}(\log (T/f) + \sqrt{f})$ regret, delivering a "wait-less" online decision-making process that balances the computational efficiency of first-order methods and the superior regret guarantee of LP-based methods.