A Nonparametric Framework for Online Stochastic Matching with Correlated Arrivals
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The design of online policies for stochastic matching and revenue management settings is usually bound by the Bayesian prior that the demand process is formed by a fixed-length sequence of queries with unknown types, each drawn independently. This assumption of serial independence implies that the demand of each type, i.e., the number of queries of a given type, has low variance and is approximately Poisson-distributed. Thus, matching policies are often based on "fluid" LPs that only use the expectations of these distributions. This paper explores alternative stochastic models for online matching that allow for nonparametric, higher variance demand distributions. We propose two new models, INDEP and CORREL, that relax the serial independence assumption in different ways by combining a nonparametric distribution for the demand with standard assumptions on the arrival patterns – adversarial or random-order. In our INDEP model, the demand for each type follows an arbitrary distribution, while being mutually independent across different types. In our CORREL model, the total demand follows an arbitrary distribution, and conditional on the sequence length, the type of each query is drawn independently. In both settings, we show that the fluid LP relaxation based on only expected demands can be an arbitrarily bad benchmark for algorithm design. We develop tighter LP relaxations for the INDEP and CORREL models that leverage the exact distribution of the demand, leading to matching algorithms that achieve constant-factor performance guarantees under adversarial and random-order arrivals. More broadly, our paper provides a data-driven framework for expressing demand uncertainty (i.e., variance and correlations) in online stochastic matching models.
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