Satisficing with Binary Feedback: Multi-User mmWave Beam and Rate Adaptation via Combinatorial Bandits

We study downlink beam and rate adaptation in a multi-user mmWave MISO system where multiple base stations (BSs), each using analog beamforming from finite codebooks, serve multiple single-antenna user equipments (UEs) with a unique beam per UE and discrete data transmission rates. BSs learn about transmissions success based on ACK/NACK feedback. To encode service goals, we introduce a satisficing throughput threshold $\tau_r$ and cast joint beam and rate adaptation as a combinatorial semi-bandit over beam-rate tuples. Within this framework we propose SAT-CTS, a lightweight, threshold-aware policy that blends conservative confidence estimates with posterior sampling, steering learning toward meeting $\tau_r$ rather than merely maximizing. We evaluate the performance via cumulative satisficing regret to $\tau_r$ alongside standard regret and fairness. Experiments under time varying sparse multipath channels show that SAT-CTS consistently reduces satisficing regret and maintains competitive standard regret, while achieving favorable average throughput and fairness across users, indicating that modest, feedback-efficient learning can equitably allocate beams and rates to meet QoS targets without channel state knowledge.