Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates
This addresses a practical bottleneck for practitioners in scalable Bayesian inference, though it is incremental as it builds on existing ParVI frameworks.
The paper tackles the problem of hyperparameter tuning in particle-based variational inference methods by introducing learning-rate-free algorithms based on coin betting, achieving comparable performance to existing methods without requiring learning rate tuning.
In recent years, particle-based variational inference (ParVI) methods such as Stein variational gradient descent (SVGD) have grown in popularity as scalable methods for Bayesian inference. Unfortunately, the properties of such methods invariably depend on hyperparameters such as the learning rate, which must be carefully tuned by the practitioner in order to ensure convergence to the target measure at a suitable rate. In this paper, we introduce a suite of new particle-based methods for scalable Bayesian inference based on coin betting, which are entirely learning-rate free. We illustrate the performance of our approach on a range of numerical examples, including several high-dimensional models and datasets, demonstrating comparable performance to other ParVI algorithms with no need to tune a learning rate.