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Configuration knobs of database systems are essential to achieve high throughput and low latency. Recently, automatic tuning systems using machine learning methods (ML) have shown to find better configurations compared to experienced database administrators (DBAs). However, there are still gaps to apply the existing systems in production environments, especially in the cloud. First, they conduct tuning for a given workload within a limited time window and ignore the dynamicity of workloads and data. Second, they rely on a copied instance and do not consider the availability of the database when sampling configurations, making the tuning expensive, delayed, and unsafe. To fill these gaps, we propose OnlineTune, which tunes the online databases safely in changing cloud environments. To accommodate the dynamicity, OnlineTune embeds the environmental factors as context feature and adopts contextual Bayesian Optimization with context space partition to optimize the database adaptively and scalably. To pursue safety during tuning, we leverage the black-box and the white-box knowledge to evaluate the safety of configurations and propose a safe exploration strategy via subspace adaptation.%, greatly decreasing the risks of applying bad configurations. We conduct evaluations on dynamic workloads from benchmarks and real-world workloads. Compared with the state-of-the-art methods, OnlineTune achieves 14.4%~165.3% improvement on cumulative performance while reducing 91.0%~99.5% unsafe configuration recommendations.