Boosting Variational Inference With Locally Adaptive Step-Sizes
This work addresses the high resource demands for practitioners using Boosting Variational Inference to obtain better posterior approximations, representing an incremental improvement in computational efficiency.
The paper tackles the computational inefficiency of Boosting Variational Inference by analyzing the global curvature of the KL-divergence and proposes a locally adaptive step-size method with a novel backtracking algorithm, achieving improved convergence rates and experimental validation on synthetic and real-world datasets.
Variational Inference makes a trade-off between the capacity of the variational family and the tractability of finding an approximate posterior distribution. Instead, Boosting Variational Inference allows practitioners to obtain increasingly good posterior approximations by spending more compute. The main obstacle to widespread adoption of Boosting Variational Inference is the amount of resources necessary to improve over a strong Variational Inference baseline. In our work, we trace this limitation back to the global curvature of the KL-divergence. We characterize how the global curvature impacts time and memory consumption, address the problem with the notion of local curvature, and provide a novel approximate backtracking algorithm for estimating local curvature. We give new theoretical convergence rates for our algorithms and provide experimental validation on synthetic and real-world datasets.