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Best of Many in Both Worlds: Online Resource Allocation with Predictions under Unknown Arrival Model

Online decision-makers often obtain predictions on future variables, such as arrivals, demands, inventories, and so on. These predictions can be generated from simple forecasting algorithms for univariate time-series, all the way to state-of-the-art machine learning models that leverage multiple time-series and additional feature information. However, the prediction accuracy is unknown to decision-makers a priori, hence blindly following the predictions can be harmful. In this paper, we address this problem by developing algorithms that utilize predictions in a manner that is robust to the unknown prediction accuracy. We consider the Online Resource Allocation Problem, a generic model for online decision-making, in which a limited amount of resources may be used to satisfy a sequence of arriving requests. Prior work has characterized the best achievable performances when the arrivals are either generated stochastically (i.i.d.) or completely adversarially, and shown that algorithms exist which match these bounds under both arrival models, without `knowing'' the underlying model. To this backdrop, we introduce predictions in the form of shadow prices on each type of resource. Prediction accuracy is naturally defined to be the distance between the predictions and the actual shadow prices. We tightly characterize, via a formal lower bound, the extent to which any algorithm can optimally leverage predictions (that is, to follow'' the predictions when accurate, and `ignore'' them when inaccurate) without knowing the prediction accuracy or the underlying arrival model. Our main contribution is then an algorithm which achieves this lower bound. Finally, we empirically validate our algorithm with a large-scale experiment on real data from the retailer H&M.

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