Online Learning for Closed-Loop Delay-Constrained Metaverse Systems: A Two-Time-Scale Approach

Wireless metaverse applications require tight coupling between haptic delay constraints and multimodal synchronization, creating a trade-off between immersion, reliability, and spectrum efficiency over time-varying channels. We propose a two-Time-scale resource allocation framework for closed-loop remote operation. At the fast time scale, downlink bandwidth is adapted per cycle via constrained online convex optimization (COCO) to minimize spectrum cost under long-Term delay constraints for haptic and multimodal traffic. At the slow time scale, visual payload is selected using an adversarial multi-Armed bandit (EXP3) under non-stationary rewards. Numerical results show the proposed framework achieves near-benchmark spectrum efficiency while steering toward delay-feasible operating points that maximize the long-Term immersive performance.