Multi-User mmWave Beam and Rate Adaptation via Combinatorial Satisficing Bandits

2026-04-16

AI Summary

This work addresses the challenge of ensuring quality-of-service (QoS) in multi-user millimeter-wave MISO systems under unknown channel conditions. The authors formulate the joint beamforming and discrete rate adaptation problem as a combinatorial semi-bandit with a satisfaction threshold τ_r, and propose SAT-CTS, a lightweight algorithm that integrates conservative upper confidence bounds with posterior sampling to prioritize meeting throughput thresholds over maximizing throughput alone. The study provides the first finite-time regret guarantees for this class of problems: when τ_r is achievable, the cumulative satisfaction regret remains constant; otherwise, the standard regret scales as O((log T)²), while maintaining fairness and feedback efficiency. Experiments demonstrate that SAT-CTS significantly reduces satisfaction regret without requiring channel state information and outperforms baseline methods in throughput, fairness, and QoS fulfillment rate.

Technology Category

• Machine Learning: Online Learning & Bandits
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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 transmission success based on ACK/NACK feedback. To encode service goals, we introduce a satisficing throughput threshold $τ_r$ 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 $τ_r$ rather than merely maximizing. Our main theoretical contribution provides the first finite-time regret bounds for combinatorial semi-bandits with satisficing objective: when $τ_r$ is realizable, we upper bound the cumulative satisficing regret to the target with a time-independent constant, and when $τ_r$ is non-realizable, we show that SAT-CTS incurs only a finite expected transient outside committed CTS rounds, after which its regret is governed by the sum of the regret contributions of restarted CTS rounds, yielding an $O((\log T)^2)$ standard regret bound. On the practical side, we evaluate the performance via cumulative satisficing regret to $τ_r$ alongside standard regret and fairness. Experiments with 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 feedback-efficient learning can equitably allocate beams and rates to meet QoS targets without channel state knowledge.

Problem

• mmWave
• beam adaptation
• rate adaptation
• satisficing
• multi-user

Innovation

• satisficing bandits
• mmWave beamforming
• combinatorial semi-bandit
• rate adaptation
• QoS-aware learning