  Millimeter-wave vehicular networks incur enormous beam-training overhead to
enable narrow-beam communications. This paper proposes a learning and
adaptation framework in which the dynamics of the communication beams are
learned and then exploited to design adaptive beam-tracking and training with
low overhead: on a long-timescale, a deep recurrent variational autoencoder
(DR-VAE) uses noisy beam-training feedback to learn a probabilistic model of
beam dynamics and enable predictive beam-tracking; on a short-timescale, an
adaptive beam-training procedure is formulated as a partially observable (PO-)
Markov decision process (MDP) and optimized via point-based value iteration
(PBVI) by leveraging beam-training feedback and a probabilistic prediction of
the strongest beam pair provided by the DR-VAE. In turn, beam-training feedback
is used to refine the DR-VAE via stochastic gradient ascent in a continuous
process of learning and adaptation. The proposed DR-VAE learning framework
learns accurate beam dynamics: it reduces the Kullback-Leibler divergence
between the ground truth and the learned model of beam dynamics by 95% over the
Baum-Welch algorithm and a naive learning approach that neglects feedback
errors. Numerical results on a line-of-sight (LOS) scenario with multipath
reveal that the proposed dual timescale approach yields near-optimal spectral
efficiency, and improves it by 130% over a policy that scans exhaustively over
the dominant beam pairs, and by 20% over a state-of-the-art POMDP policy.
Finally, a low-complexity policy is proposed by reducing the POMDP to an
error-robust MDP, and is shown to perform well in regimes with infrequent
feedback errors.
