We propose an efficient mobility management solution to the problem of assigning small base stations (SBSs) to multiple mobile data users in a heterogeneous setting. We formalize the problem using a novel sequential decision-making model named contextual combinatorial volatile multi-armed bandits (MABs), in which each association is considered as an arm, volatility of an arm is imposed by the dynamic arrivals of the users, and context is the additional information linked with the user and the SBS such as user/SBS distance and the transmission frequency. As the next-generation communications are envisioned to take place over highly dynamic links such as the millimeter wave (mmWave) frequency band, we consider the association problem over an unknown channel distribution with a limited feedback in the form of acknowledgments and under the absence of channel state information (CSI). As the links are unknown and dynamically varying, the assignment problem cannot be solved offline. Thus, we propose an online algorithm which is able to solve the user-SBS association problem in a multi-user and time-varying environment, where the number of users dynamically varies over time. Our algorithm strikes the balance between exploration and exploitation and achieves sublinear in time regret with an optimal dependence on the problem structure and the dynamics of user arrivals and departures. In addition, we demonstrate via numerical experiments that our algorithm achieves significant performance gains compared to several benchmark algorithms.

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We consider the problem of optimizing a vector-valued objective function f sampled from a Gaussian Process (GP) whose index set is a well-behaved, compact metric space (X , d) of designs. We assume that f is not known beforehand and that evaluating f at design x results in a noisy observation of f (x). Since identifying the Pareto optimal designs via exhaustive search is infeasible when the cardinality of X is large, we propose an algorithm, called Adaptive -PAL, that exploits the smoothness of the GP-sampled function and the structure of (X , d) to learn fast. In essence, Adaptive -PAL employs a tree-based adaptive discretization technique to identify an -accurate Pareto set of designs in as few evaluations as possible. We provide both information-type and metric dimension-type bounds on the sample complexity of -accurate Pareto set identification. We also experimentally show that our algorithm outperforms other Pareto set identification methods on several benchmark datasets.Preprint. Under review.