Beyond O(√T) Regret: Decoupling Learning and Decision-making in Online Linear Programming

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 O ( √T ), which is suboptimal compared to the O (log T) bound guaranteed by the state-of-the-art linear programming (LP)-based online algorithms. This paper establishes a general framework that improves upon the O ( √T ) result when the LP dual problem exhibits certain error bound conditions. For the first time, we show that first-order learning algorithms achieve o( √T ) regret in the continuous support setting and O (log T) regret in the finite support setting beyond the non-degeneracy assumption. Our results significantly improve the state-of-the-art regret results and provide new insights for sequential decision-making.