Online Resource Allocation without Re-solving: The Effectiveness of Primal-Dual Policies

Abstract

We study an online resource allocation problem where requests arrive sequentially over time and must be served immediately and irrevocably under resource constraints. While state-of-the-art policies, such as probabilistic resolving (PR) (Balseiro et al., 2024) and the Bayes selector (Vera and Banerjee, 2021), achieve constant regret, they may require resolving large-scale linear programs (LPs) many times, making them computationally expensive. In this paper, we propose a simple primal-dual policy that requires solving the fluid linear program only once upfront and then uses dynamic dual variable updates to reflect real-time resource availability. Under a general position gap condition equivalent to existing non-degeneracy assumptions, we prove that our policy achieves constant regret independent of the time horizon-the first such guarantee for primal-dual policies in online resource allocation. Our analysis reveals that by adjusting dual variables based on actual resource consumption, the policy maintains a negative drift that pulls the dual variables back toward optimality when they deviate significantly. The policy is computationally efficient, interpretable, and well-suited for distributed implementation as resource constraints are replaced with shadow prices that guide decision-making.

Keywords: Online resource allocation, Primal-dual policies, General position gap, Constant regret