Dynamic online convex optimization with long-term constraints via virtual queue

Abstract In this paper, we investigate the online convex optimization (OCO) with long-term constraints which is widely used in various resource allocations and recommendation systems. Different from the most existing works, our work adopts a dynamic benchmark to analyze the optimization performance since the dynamic benchmark is more common than the static benchmark in practical applications. Moreover, compared with many constrained OCO works ignoring the Slater condition, we study the effect of the Slater condition on the constraint violation bounds and obtain the better performance of the constraint violations when the Slater condition holds. More importantly, we propose a novel iterative optimization algorithm based on the virtual queues to achieve sublinear regret and constraint violations. Finally, we apply our dynamic OCO model to a resource allocation problem in cloud computing and the results of the experiments validate the effectiveness of our algorithm.