Linear Convergence of Black-Box Variational Inference: Should We Stick the Landing?

arXiv:2307.14642v3 Announce Type: replace-cross
Abstract: We prove that black-box variational inference (BBVI) with control variates, particularly the sticking-the-landing (STL) estimator, converges at a geometric (traditionally called "linear") rate under perfect variational family specification. In particular, we prove a quadratic bound on the gradient variance of the STL estimator, one which encompasses misspecified variational families. Combined with previous works on the quadratic variance condition, this directly implies convergence of BBVI with the use of projected stochastic gradient descent. For the projection …

abstract arxiv box control convergence cs.lg family gradient inference landing linear prove rate stat.co stat.ml stl type variance