Reinforcement Learning With Conformal Symplectic Optimization for Aerial RIS-Aided Secure Communication

This paper investigates a secure aerial reconfigurable intelligent surface (A-RIS) communication system, where user mobility, imperfect channel state information (CSI), and RIS phase errors induced by unmanned aerial vehicle (UAV) jitter significantly degrade performance. To address these challenges, we formulate a joint optimization problem for UAV trajectory, base station (BS) we propose abeamforming, and A-RIS beamforming to maximize the minimum secrecy energy efficiency (SEE), subject to constraints on user secrecy rates and UAV energy efficiency. To solve this highly non-convex problem, we propose a novel reinforcement learning framework termed IA-CSORL based on the twin-twin-delayed deep deterministic policy gradient (TTD3) architecture, which incorporates two novel modules. Specifically, we develop the phase-aware relativistic adaptive descent (PRAD) algorithm is proposed, which embeds the learning process into a conformal Hamiltonian system. By integrating gradient-based phase error correction and adaptive momentum adjustment, PRAD effectively counteracts phase noise and stabilizes training. Furthermore, we design an environment-state interactive attention (ESIA) mechanism to dynamically fuse UAV positioning and environmental features, enhancing state representation and deployment accuracy. Numerical results demonstrate that IA-CSORL significantly outperforms existing RL baselines in terms of both robustness and convergence performance. Moreover, IA-CSORL achieves superior beamforming accuracy under phase errors and CSI imperfections and provides a better trade-off between sum secrecy rate (SSR) and SEE, with performance gains becoming more significant as the number of RIS elements increases.