We propose a beam alignment algorithm that enables initial access establishment between two transceivers equipped with hybrid digital-analog antenna arrays operating in millimeter wave wireless channels. The proposed method builds upon an active channel learning method based on hierarchical posterior matching that was originally proposed for single-sided beam alignment on single path dominant channels. We extend it to the double-sided alignment problem and propose an estimation framework based on variational Bayesian inference that accounts for the uncertainties on the unknown channel complex gain and noise variance. The proposed approach is numerically shown to be resilient to the single path assumption and reaches near optimal beamforming gains with a moderate training overhead, even at low signal-to-noise ratios.