Decoupling Learning and Decision-Making: Breaking the
$\mathcal{O}(\sqrt{T})$ Barrier in Online Resource Allocation with
First-Order Methods
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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. More importantly, for the first time, we show that first-order methods can attain regret $\mathcal{O}(T^{1/3})$ with this new framework. Lastly, we conduct numerical experiments to validate our theoretical findings.Keywords:
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Abstract As the development of computer science technology and the requirement of thorough research, more researchers are setting their eyes on coupling method because of the tight coupling in NPP (nuclear power plant) system. However there were few researches studying the difference between decoupling and coupling methods and the importance of coupling method. This research respectively establishes the primary and secondary loop decoupling models and the two loops coupling model based on the small NPP by APROS. Then the differences between the decoupling and coupling models is studied under the steady state and dynamic state which contains the ramp load variation and load shedding. The results show that there are small differences between these models in the main parameter values under the steady state. But the differences between decoupling models and coupling model are large. Therefore the NPP system needs be modeled by coupling method as to study its dynamic characteristic.
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