A Proofs

First, we recall basic properties of convex conjugate functions that we rely on in our proofs. The latter condition holds, e.g., for strongly convex functions. For each n = 1, 2,...,N we perform the following evaluation: ξ W First, we prove the congruence, i.e., βψ We provide the hyperparameters of all the experiments with algorithm 1 in Table 3. We use Adam optimizer with the default betas. Gaussian case, we use a single GPU GTX 1080ti.