Many real-world sequential decision-making problems involve critical systems that present both human-life and financial risks. While several works in the past have proposed methods that are safe for deployment, they assume that the underlying problem is stationary. However, many real-world problems of interest exhibit non-stationarity, and when stakes are high, the cost associated with a false stationarity assumption may be unacceptable. Addressing safety in the presence of non-stationarity remains an open question in the literature. We present a type of Seldonian algorithm (Thomas et al., 2019), taking the first steps towards ensuring safety, with high confidence, for smoothly varying non-stationary decision problems, through a synthesis of model-free reinforcement learning algorithms with methods from time-series analysis.