The proliferation of the Internet of Everything (IoE) necessitates efficient Probabilistic Skyline (PSKY) query analytics at the network edge, which is severely constrained by the trade-off between limited computational capacity and high-variance communication bandwidth. Conventional static thresholding and heuristic-based approaches fail to adapt to the inherent volatility and non-independent and identically distributed (non-IID) characteristics of edge streams, often triggering network congestion or compromising query fidelity. To address these systemic inefficiencies, this paper introduces SA-PSKY, a self-adaptive framework integrating deep reinforcement learning into a distributed query optimization architecture. We model threshold selection as a continuous-space Markov Decision Process (MDP) and develop a State-Aware Adaptive Weighting (SAAW) mechanism to facilitate autonomous, fine-grained filtering. By incorporating Prioritized Experience Replay (PER) as a stabilization guardrail, our framework reliably navigates the Pareto frontier between local computational overhead and global system responsiveness. Empirical evaluations confirm that SA-PSKY significantly outperforms baselines, including DQN, PPO, and TD3, achieving an average end-to-end latency reduction of 70%. Furthermore, zero-shot generalization analyses reveal superior scalability, as SA-PSKY maintains stable performance under unseen data distributions where rigid methods suffer from catastrophic policy failure. These findings validate SA-PSKY as a resilient, scalable architectural paradigm for real-time analytics within heterogeneous edge-cloud ecosystems.

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