Decentralized online integer programming problems with a coupling cardinality constraint

Abstract

We consider a problem involving a set of agents who need to coordinate their actions to optimize the sum of their objectives while satisfying a common resource constraint. The objective functions of the agents are unknown to them a priori and are revealed in an online manner. The resulting problem is an online optimization problem to optimally allocate the resource among the agents prior to observing the item values. For any deterministic online algorithm for this problem, it has been shown that there exists a lower bound of Ω(T ) on regret. When the agents’ integer programs satisfy a discrete concavity condition, we propose a randomized online algorithm that is decentralized and guarantees an upper bound of O( √ T ) on the expected regret.