Bayesian Bandit Beamforming with Implicit Channel Learning for RIS under Hybrid Near/Far-Field Propagation

Reconfigurable intelligent surfaces (RISs) can improve high-frequency wireless links by shaping the propagation environment, but their passive architecture makes channel acquisition costly. Conventional estimate-then-optimize methods usually require pilot overhead that scales with the number of reflecting elements, which is undesirable under short coherence times and hybrid near-/far-field propagation. This paper proposes the Bayesian bandit framework for RIS phase-shift configuration with implicit channel learning. The method updates a Gaussian posterior of the cascaded channel from one scalar pilot observation per slot and uses Thompson sampling to balance channel estimation and beamforming gain. We derive a Bayesian regret decomposition that connects Bayesian received-power regret to posterior uncertainty contraction, and further establish a conditional sublinear Bayesian-regret guarantee. To exploit sparse hybrid-field propagation, we develop an energy-focusing angle-distance dictionary and a sparse Bayesian learning (SBL)-based Thompson-sampling algorithm with warm-started hyperparameter refinement. Simulations show that the proposed policies approach the perfect-channel state information (CSI) benchmark in the line-of-sight (LOS)-dominant setting within 10 time block and improve transmission efficiency over the considered baselines in multipath and Rayleigh fading scenarios.