Adaptive Online Resource Allocation Schemes under General Non-Stationary Arrivals

Abstract

We propose a novel first-order method for online resource allocation under a non-stationary arrival process and unknown demands. We assume multiple types of customers arrive in a nonstationary stochastic fashion, with unknown arrival rates in each period. It is also assumed that customers' click-through rates are unknown and can only be learned online. By leveraging results from the stochastic contextual bandit with knapsack and online matching with adversarial arrivals, we develop an online scheme to allocate the resources to nonstationary customers, which is adaptive to the non-stationarity of the customer arrival process. We prove that under mild conditions, our scheme enjoys a "best-of-both-world" guarantee: the scheme has a sublinear regret when the customer arrivals are near-stationary, and has an optimal competitive ratio under general (non-stationary) customer arrival distributions. Finally, we conduct extensive numerical experiments to show that our approach generates near-optimal revenues under general non-stationary arrivals.