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

2024-12-12

AI Summary

Online linear programming (OLP) faces a fundamental trade-off between computational efficiency and regret minimization. Method: We propose a synergistic framework combining periodic LP re-solving with parallel first-order optimization. Our “wait-free” architecture periodically invokes an offline LP solver to obtain high-precision dual prices, while concurrently performing parallel gradient updates to smooth resource consumption and mitigate decision latency; dual price migration and periodic synchronization ensure theoretical consistency. Contribution/Results: We establish the first regret bound of $O(log(T/f) + sqrt{f})$ achievable in nearly linear time—significantly improving upon traditional LP-based methods (high computational overhead) and pure first-order approaches (large regret). Experiments demonstrate strong scalability and efficacy in large-scale, real-time revenue management and dynamic resource allocation tasks.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• 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

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.

Problem

• Online Linear Programming
• Computational Efficiency
• Regret Guarantees

Innovation

• Online Linear Programming
• Dual Prices
• First-Order Methods