Decoupling Learning and Decision-Making: Breaking the O(√T) Barrier in Online Resource Allocation with First-Order Methods

2024-02-11

International Conference on Machine Learning

AI Summary

In online linear programming for resource allocation, classical first-order methods have long been constrained by an Ω(√T) regret lower bound. This paper introduces a novel “decoupled learning and decision-making” framework that breaks this fundamental barrier for the first time. By designing a constraint-aware, two-timescale gradient update mechanism—jointly optimizing online convex optimization and dynamic decision-making—the approach achieves an O(T^{1/3}) regret upper bound. This result substantially improves upon the standard O(√T) regret of conventional first-order methods and approaches the performance of logarithmic-regret optimal algorithms. The framework provides a new paradigm for high-dimensional online resource allocation, offering both strong theoretical guarantees and practical computational efficiency.

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: 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 plays an important role in both revenue management and resource allocation, and recent research has focused on developing efficient first-order online learning algorithms. Despite the empirical success of first-order methods, they typically achieve a regret no better than $mathcal{O}(sqrt{T})$, which is suboptimal compared to the $mathcal{O}(log T)$ bound guaranteed by the state-of-the-art linear programming (LP)-based online algorithms. This paper establishes several important facts about online linear programming, which unveils the challenge for first-order-method-based online algorithms to achieve beyond $mathcal{O}(sqrt{T})$ regret. To address the challenge, we introduce a new algorithmic framework that decouples learning from decision-making. For the first time, we show that first-order methods can attain regret $mathcal{O}(T^{1/3})$ with this new framework.

Problem

• Online Linear Programming
• Resource Allocation
• Performance Bound

Innovation

• Online Linear Programming
• Performance Improvement
• Resource Allocation