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Provable convergence guarantees for black-box variational inference. (arXiv:2306.03638v1 [cs.LG])

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While black-box variational inference is widely used, 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 the first rigorous guarantee that
black-box variational inference converges for realistic inference problems.

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