The paper introduces Rényi Differential Privacy (RDP), a relaxation of the standard differential privacy definition based on the Rényi divergence. RDP is argued to be a more accurate and flexible measure of privacy guarantees, particularly for composite heterogeneous mechanisms. The authors demonstrate that RDP shares many key properties with differential privacy, such as robustness to auxiliary information and preservation under adaptive sequential composition. They also show that RDP can be used to derive advanced composition theorems, providing tighter bounds on privacy loss in composite mechanisms. The paper includes a detailed analysis of basic mechanisms like randomized response, Laplace, and Gaussian noise addition, and compares the RDP guarantees with those of $(\epsilon, \delta)$-differential privacy. The results highlight the advantages of RDP in terms of tighter bounds and easier analysis, especially for probabilities smaller than $\delta$. The paper concludes with a discussion on the practical implications of RDP and its potential applications in privacy-preserving algorithms.The paper introduces Rényi Differential Privacy (RDP), a relaxation of the standard differential privacy definition based on the Rényi divergence. RDP is argued to be a more accurate and flexible measure of privacy guarantees, particularly for composite heterogeneous mechanisms. The authors demonstrate that RDP shares many key properties with differential privacy, such as robustness to auxiliary information and preservation under adaptive sequential composition. They also show that RDP can be used to derive advanced composition theorems, providing tighter bounds on privacy loss in composite mechanisms. The paper includes a detailed analysis of basic mechanisms like randomized response, Laplace, and Gaussian noise addition, and compares the RDP guarantees with those of $(\epsilon, \delta)$-differential privacy. The results highlight the advantages of RDP in terms of tighter bounds and easier analysis, especially for probabilities smaller than $\delta$. The paper concludes with a discussion on the practical implications of RDP and its potential applications in privacy-preserving algorithms.