Fast Black-box Variational Inference through Stochastic Trust-Region Optimization
This addresses the need for faster and more reliable variational inference methods in machine learning, though it is incremental as it builds on existing second-order and trust-region techniques.
The authors tackled the problem of slow convergence in black-box variational inference by introducing TrustVI, a second-order algorithm using trust-region optimization and reparameterization, which converged at least 10 times faster than ADVI and found better variational distributions than HFSGVI.
We introduce TrustVI, a fast second-order algorithm for black-box variational inference based on trust-region optimization and the reparameterization trick. At each iteration, TrustVI proposes and assesses a step based on minibatches of draws from the variational distribution. The algorithm provably converges to a stationary point. We implemented TrustVI in the Stan framework and compared it to two alternatives: Automatic Differentiation Variational Inference (ADVI) and Hessian-free Stochastic Gradient Variational Inference (HFSGVI). The former is based on stochastic first-order optimization. The latter uses second-order information, but lacks convergence guarantees. TrustVI typically converged at least one order of magnitude faster than ADVI, demonstrating the value of stochastic second-order information. TrustVI often found substantially better variational distributions than HFSGVI, demonstrating that our convergence theory can matter in practice.