Riemannian Black Box Variational Inference

We introduce Riemannian Black Box Variational Inference for scenarios lacking gradient information of the model with respect to its parameters. Our method constrains posterior marginals to exponential families, optimizing variational free energy using Riemannian geometry and gradients of the log-partition function. It excels with black-box or nondifferentiable models, where popular methods fail. We demonstrate efficacy through the inference of parameters from the SIR model and the tuning of neural network learning rates. The results show competitive performance with gradient-based (NUTS) and gradient-free (Latent Slice Sampling) methods, achieving better coverage and matching Bayesian optimization with fewer evaluations. This extends variational inference to settings where model gradients are unavailable, improving efficiency and flexibility for real-world applications.