Intelligent manufacturing applications and agent-based implementations are scientifically investigated due to the enormous potential of industrial process optimization. The most widespread data-driven approach is the use of experimental history under test conditions for training, followed by execution of the trained model. Since factors, such as tool wear, affect the process, the experimental history has to be compiled extensively. In addition, individual machine noise implies that the models are not easily transferable to other (theoretically identical) machines. In contrast, a continual learning system should have the capacity to adapt (slightly) to a changing environment, e.g., another machine under different working conditions. Since this adaptation can potentially have a negative impact on process quality, especially in industry, safe optimization methods are required. In this article, we present a significant step towards self-optimizing machines in industry, by introducing a novel method for efficient safe contextual optimization and continuously trading-off between exploration and exploitation. Furthermore, an appropriate data discard strategy and local approximation techniques enable continual optimization. The approach is implemented as generic software module for an industrial edge control device. We apply this module to a steel straightening machine as an example, enabling it to adapt safely to changing environments.