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The classic newsvendor model yields an optimal decision for a "newsvendor"selecting a quantity of inventory, under the assumption that the demand isdrawn from a known distribution. Motivated by applications such as cloudprovisioning and staffing, we consider a setting in which newsvendor-typedecisions must be made sequentially, in the face of demand drawn from astochastic process that is both unknown and nonstationary. All prior work onthis problem either (a) assumes that the level of nonstationarity is known, or(b) imposes additional statistical assumptions that enable accurate predictionsof the unknown demand.  We study the Nonstationary Newsvendor, with and without predictions. Wefirst, in the setting without predictions, design a policy which we prove (viamatching upper and lower bounds) achieves order-optimal regret -- ours is thefirst policy to accomplish this without being given the level ofnonstationarity of the underlying demand. We then, for the first time,introduce a model for generic (i.e. with no statistical assumptions)predictions with arbitrary accuracy, and propose a policy that incorporatesthese predictions without being given their accuracy. We upper bound the regretof this policy, and show that it matches the best achievable regret had theaccuracy of the predictions been known. Finally, we empirically validate ournew policy with experiments based on two real-world datasets containingthousands of time-series, showing that it succeeds in closing approximately 74%of the gap between the best approaches based on nonstationarity and predictionsalone.

The Nonstationary Newsvendor with (and without) Predictions