  Energy efficient mobility management is an important problem in modern
wireless networks with heterogeneous cell sizes and increased nodes densities.
We show that optimization-based mobility protocols cannot achieve long-term
optimal energy consumption, particularly for ultra-dense networks (UDN). To
address the complex dynamics of UDN, we propose a non-stochastic
online-learning approach which does not make any assumption on the statistical
behavior of the small base station (SBS) activities. In addition, we introduce
handover cost to the overall energy consumption, which forces the resulting
solution to explicitly minimize frequent handovers. The proposed Batched
Randomization with Exponential Weighting (BREW) algorithm relies on batching to
explore in bulk, and hence reduces unnecessary handovers. We prove that the
regret of BREW is sublinear in time, thus guaranteeing its convergence to the
optimal SBS selection. We further study the robustness of the BREW algorithm to
delayed or missing feedback. Moreover, we study the setting where SBSs can be
dynamically turned on and off. We prove that sublinear regret is impossible
with respect to arbitrary SBS on/off, and then develop a novel learning
strategy, called ranking expert (RE), that simultaneously takes into account
the handover cost and the availability of SBS. To address the high complexity
of RE, we propose a contextual ranking expert (CRE) algorithm that only assigns
experts in a given context. Rigorous regret bounds are proved for both RE and
CRE with respect to the best expert. Simulations show that not only do the
proposed mobility algorithms greatly reduce the system energy consumption, but
they are also robust to various dynamics which are common in practical
ultra-dense wireless networks.
