Provable convergence guarantees for black-box variational inference
Black-box variational inference is widely used in situations where there is no proof that its stochastic optimization succeeds. We suggest this is due to a theoretical gap in existing stochastic optimization proofs: namely the challenge of gradient estimators with unusual noise bounds, and a composite non-smooth objective. For dense Gaussian variational families, we observe that existing gradient estimators based on reparameterization satisfy a quadratic noise bound and give novel convergence guarantees for proximal and projected stochastic gradient descent using this bound. This provides rigorous guarantees that methods similar to those used in practice converge on realistic inference problems.
Code (0)
등록된 구현이 없습니다.
Tasks
Stochastic OptimizationVariational InferenceMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Provable Smoothness Guarantees for Black-Box Variational Inference
Black-box variational inference tries to approximate a complex target distribution though a gradient-based optimization of the parameters of a simpler distribution. Provable convergence guarantees require structural prop…
Variational InferenceProvable Gradient Variance Guarantees for Black-Box Variational Inference
Recent variational inference methods use stochastic gradient estimators whose variance is not well understood. Theoretical guarantees for these estimators are important to understand when these methods will or will not w…
Variational InferenceAsymptotically exact variational flows via involutive MCMC kernels
Most expressive variational families -- such as normalizing flows -- lack practical convergence guarantees, as their theoretical assurances typically hold only at the intractable global optimum. In this work, we present …
On the Convergence of Black-Box Variational Inference
We provide the first convergence guarantee for full black-box variational inference (BBVI), also known as Monte Carlo variational inference. While preliminary investigations worked on simplified versions of BBVI (e.g., b…
Bayesian InferenceVariational InferenceFast Black-box Variational Inference through Stochastic Trust-Region Optimization
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 o…
Variational Inference